A lot of the answers you've already received address questions like "what is the benefit to trade" or "why do we have specialization of labor." I think this is a little more basic than what you asked--I'm assuming you meant not 'why do we have an economy' but "why do we need to 'get the economy moving again' right now", rather than five (ten, twenty...) years down the road--i.e. what are the arguments for removing barriers to pre-disease economic activity as soon as possible and for providing incentives to "encourage" people back to work, who would rather wait until things are known to be safer. (You probably implicitly assume that the economy will 'get moving again' at some point--if it doesn't, then... well... it doesn't; I assume you aren't asking 'why should we go back to the status quo ante' and that you accept that returning spontaneously to the exact economic status from before the disease would require a very long time, if it happens at all).
First, let me point out: economics as a discipline is not about value judgments. It's about the production and distribution of goods under various policy regimes, and thus predicting the effects of policy decisions on same. Whether the effects are desirable or not is a political decision which requires assigning values outside the economic discipline.
So. Why now?
This answer has two parts: first, what are some predicted effects of longer shutdowns that might be avoided by shorter ones, and second, from a political (ie, non-economic) standpoint, what are some motivations for different parties that might motivate particular courses of action. The latter section will be more opinionated and controversial than the former, but I am including it because a) it's where the answer to your question actually lies, and b) part of what makes economics such a privileged discipline in our society is that economics-the-science is forever getting conflated with these sorts of political-philosophical issues; it's worthwhile making them explicit.
Effects of Longer Shutdown
The biggest consequences of longer vs. shorter shutdowns can be summarized as "loss of economic momentum." You've already noted that shutdown blows a hole in tax revenues, constraining the agency of state and local governments and requiring federal government to take a more active redistribution role. The two remaining players are workers and firms.
- For workers, the longer one is unemployed, the harder it is to find a new job. (Yes, a pop source, but it's a decent summary). This comes down to two main factors: discrimination on the part of employers, and skills deterioration. In the present situation of ~15% unemployment, discrimination is less likely to be a factor. However, workers' skills will still be deteriorating, and the unemployed are being denied the opportunity for skills and career development, leading to increased competition with new graduates/young people entering the workforce. A big clog in the pipeline means a dearth of people at higher experience levels across the board in the future.
- For firms, it is much much easier to continue in an established business than to set up a new one. The longer businesses are shut down, the more reopening starts to resemble starting a brand-new business, with all of the corresponding challenges of getting yourself set up, finding workers to hire, making yourself known to customers, establishing relationships with suppliers, etc. This effect is particularly pronounced for small businesses, which do not have the name recognition, credit/cash reserves, or formalized supplier networks of larger firms. Think of your local family-owned auto repair shop: they have a glass supplier they trust, a parts supplier they know can get them something by tomorrow morning, claims adjusters they can point customers to; not to mention all the money they spent on ads to make people think of going to them. The longer they're shut down, the more their customers forget. The longer they're shut down, the more likely those partners go out of business, and now they can't offer the same quality service at the same prices. They may even lose key employees. This is one of the main points in the discussion of u-shaped and v-shaped recoveries--the longer you're shut down, the harder it is to come back.
Price instability occurs as a knock-on effect of the above. Modern supply chains are extended and bizarre, and as firms collapse, the distribution of goods starts to break down in unpredictable ways. A lot of this disruption is probably temporary, but our assumptions about the availability of goods can become dangerously wrong. Effects can be felt at a distance in ways we can't predict: the closure of meat-packing plants leads to culling of animals on farms, meaning that farm animal production is down; what if this means that once a vaccine is available, there are shortages of animal-derived amino acids, gelatins, etc. that prevent production?
Financial networks are also complicated. When people or firms can't pay their rent, landlords can't afford to pay their mortgages; then banks start having cash flow issues, etc. Now, the 2008-2009 crisis demonstrated clearly the federal government's ability and willingness to make the financial sector whole, so this is more a concern of political will than inevitability; but if we assume no government intervention--intervention being a policy choice many economists are unhappy with on principle--the consequences could be a breakdown in the credit system that inhibits new firm formation even after the crisis has passed.
The desirability of the above varies depending on where you're standing. Maybe you think decreased overall economic output is good for environmental reasons. Maybe you're an established player in an industry and think extra headwinds for the smaller firms you compete with are great news. Maybe you're looking forward to high unemployment so you can cut employee wages. That's all outside the scope of the economic question.
Further, while some of the above issues might be avoided by reopening faster, these consequences I've described are all also predictable results of having to shut down again or having large parts of the workforce die from coronavirus. It is no secret that minimization of or indifference to the risks of coronavirus is correlated with politically conservative views; many economists tend to share a more politically conservative outlook, particularly those who are disinclined to care about disciplines or considerations outside of economics. Thus a lot of the predictions from economists assume "reopening sooner than later, and nothing bad happens"--taking it for granted that the health risks have actually passed, and the only variable is the one we actually control (choosing to reopen). Even regardless of possible personal bias, that assumption is sort of baked into the question. The consequences of "reopening, only to shut down again after renewed viral spread" would probably be the same types as staying closed longer, but worse (because it gets dragged out even more). Which one is true? We just don't know, and the answers to that come from epidemiologists, not economists.
Final point: the consequences above can be addressed by government intervention: adjustment of financial contracts to share the burden of lost income, expanded public-sector employment opportunities and jobs training for workers, insurance programs, contracts, and incentive programs for smaller and new firms, direct spending to initiate cycles of economic growth... Due to political or other considerations, economists vary in their support of such measures, but from 1941-1945 the US government seized the lion's share of the country's GDP literally to go blow it up and the result was the largest period of sustained economic growth in the country's history, so there's certainly historical precedent that we can find non-traditional, non-laissez-faire ways to solve practical problems in the production and distribution of real goods over the medium term of a few years.
Qui Bono, or "Who's 'We'"?
The other question you've implicitly asked is who the "we" is that needs to 'get the economy moving again.' Whose interests does it serve? I once again stress that balancing the interests of competing groups in society is a political not an economic decision. Indeed, most basic (introductory-undergrad-level) economics explicitly does not consider competing interests or varying wealth distributions among different social groups, instead using representative agent models that assume uniformity among consumers, firms, etc. So let's look at who those groups might be and what their motivations might be.
Workers: Well, most Americans still want to move more slowly. Polling is complicated; people differ in their levels of desperation, indifference to or awareness of individual & group risks, etc. I'm sure you can imagine that there's diverse opinion. I'll point out a structural feature though: most workers disemployed by the shutdown can tolerate continued closure only while government support (money and rent/loan repayment freezes) are in effect. As more and more workers rejoin the workforce due to reopening (or are forced to take dangerous essential jobs because they need the money, or...) the collective interests of workers become more fractured, which will erode the political support for the measures that let people stay home, which will force more back to work... etc. It is in the interest of those who want to stay home to make that preference as widespread as possible.
Consumers: Obviously many people wish they could consume things that aren't currently available. Maybe Kate wants her haircut, even if that means half her neighborhood (or, let's be honest, not her neighborhood) catches coronavirus as a result. But overall, the same polls cited above still apply, since workers are consumers.
State and Local Governments: In addition to the generic tax revenue issue you mentioned, there's also the problem that states are running out of unemployment money (that article's from mid-April, so the situation has only gotten worse). States, unlike the federal government, actually have to pay their debts. This would be fixable with money from the feds, but given the ongoing lack of federal support, it is obviously in states' interests to promote a return to work; if workers die, all the better, one fewer unemployment check to pay.
Small firms: As I mentioned, they are most vulnerable to closure due to longer downturns. They are also struggling because relief nominally intended for them was snapped up by other parties and because massively-underpaid service work is extremely difficult to hire for when there are more generous unemployment benefits at no risk of infecting your family with coronavirus
Renters: are doing all right, given the widespread eviction freezes and rent pauses. Same goes for student debtors. Of course, this is going to explode in six months when all that back rent is due. But that's a problem for another day.
Landlords/Rentiers: are taking a bath right now, because of the eviction freezes and rent pauses. They haven't, on the whole, been getting the same level of government support that renters have. And they are definitely worried about that 'problem for another day' of a bunch of unemployed people not able to pay six months' back rent.
Large firms: The Dow Jones Industrial Average is already back above where it was 12 months ago--Wall Street either believes that reopening will be successful, or that it doesn't matter anyway, because government supports for large industries will continue as needed. After all, the biggest targeted federal government intervention to promote production during the crisis has been to free owners of liability for worker harms in meat-packing plants. Larger firms are taking this opportunity to use bankruptcy to get out of debts and unfavorable contracts, and probably see it as a good opportunity to consolidate market position by replacing the smaller firms that are getting hit harder. That's not to say there aren't some large firms that are really hurting, but we have seen plenty of political will to support e.g. the airline industry in the past and there's little reason to think that won't continue.
Psychological need: The coronavirus has meant a huge alteration in people's ability to plan for the future and control their lives. This is extremely uncomfortable for many. People naturally want to feel in control, and reopening--returning to the appearance of normalcy and comfortable daily patterns--can help many to feel like the crisis is over and they are in control of their lives again. There's also just the sheer boredom with the current state of affairs: many people are just simply impatient. Unfortunately, epidemiology does not care about your feelings; but it is my personal observation that a desire for control in one's personal life and a lived experience of substantial control over one's life (e.g., being personally well off, or usually employed in a supervisory role) correlate to a tendency both to minimize the risks posed by the virus and to promote reopening despite whatever risks are acknowledged. I am not aware of any formal work done on this and it is (obviously) not an economic consideration, but it's an undercurrent in the public conversation.
"Winners": The longer mass unemployment is the norm, the more entrenched things like rent relief and student loan debt relief will become. There are economic arguments about the sanctity of paying debts in order to create trust in the credit markets, but ultimately this concern is about the relative power of debtors and creditors (and renters vs rentiers, those who collect gains by virtue not of productive actions but by owning property). The stock market and financial industry don't seem too concerned right now, but as with the small-business-hiring issue above, you are already seeing a shift in the balance of power between labor and owners, between renters and landlords, between debtors and creditors. The longer that continues, the more it normalizes ideas like universal basic income and dramatic rent and student-debt reforms, which would not be in the interests of people whose income is chiefly derived from large current wealth and wealth inequality. Given, among many other examples, the privileged position unearned income has in the US tax code, it seems credible to believe that the interests of the wealthy are disproportionately represented by the same government figures that are pushing for a return to work.
Ultimately, you're asking why reopening needs to happen now. There are real economic consequences to a prolonged shutdown which are probably undesirable from most perspectives/value systems. However, it is not at all clear that rapid reopening solves the issue--there is a substantial risk of prolonged and worse economic impacts due to viral resurgence. To truly answer your question, we have to look outside the discipline of economics to consider the interests of different impacted parties, and how those interests are represented in our society, public culture/media discourse, and decision-making mechanisms.