I will focus on some economics reasons not mentioned explicitly so far. There are economic benefits to having your own currency. Your question essentially raises the question of so-called "Optimum Currency Areas" (OCAs). There was a lot of interest in the question of what areas should have the same currency. It is in general not immediately obvious that different countries should have the same currency, or even that the same country should have the same currency everywhere.

Your question boils down to asking whether the whole world is an OCA - and the short answer is no.

The pros of having different currencies are that you can use monetary policy to offset shocks. Especially for trade shocks, because monetary policy can change the exchange rate of a currency to affect trade. For example if Germany and France are hit by different shocks, then they will want to conduct different monetary policies, which they can't if they share the same currency. The main cost of different currencies are transaction costs of exchange, which can hamper things trade and tourism.

Therefore an area should have the same currency (is an OCA) if it is subject to the same shocks or other factors are present, such that those shocks are absorbed without monetary policy. This thinking leads us to the four most important criteria for an area to be an OCA. You can use these criteria to evaluate whether countries should have the same currency and to answer your question.

It is worth noting, that the pioneer in this literature was Robert Mundell with his 1961 paper. The other two most important works are Kenen (1969) and Mckinnon (1963). The criteria are:


1. The regions should have similar business cycles. As mentioned, if the countries tend to experiene similar shocks, then they will require the same monetary policy. In that case there is no reason for them to have different currencies!
 
2. Openness of the economy (Mckinnon). This can be divided in two parts:

2.1. High labor mobility across regions. If there is a recession in one region and people can move to another one as a response, then monetary policy is less important in adjusting to the shock, as labor itself adjusts. This is a reason why countries can usually have the same currency within their whole territory. For example, people who lose their job in one U.S. state often move to another. If that wouldn't be possible, then adjusting to the recession with monetary policy would be more important. That is why the freedom of movement agreement is so important for the Euro to be sustainable. Note that wage flexibility would be required here as well.

2.2. Capital mobility. The reasons are similar as for labor mobility. If a region becomes less developed, then returns to capital there will increase. If markets are free, then capital can travel from the more prosperous region to the one hit by the shock, thereby mitigating the negative effects of the shock. Note that price flexibility must be given here for these effects to occur.

3. A risk sharing system, such as fiscal transfers. Since monetary policy can't be used, we would need fiscal policy. Fiscal transfers from unaffected areas can help with negative shocks in another region. The Eurozone has a no-bailout clause, so this condition wasn't given during the Greek crisis. However, this was de facto abandoned. This is unsurprising to those familiar with the theory of OCAs.

4. Product Diversity (Kenen). Trade shocks, which monetary policy can help with, usually occur to certain industries and not the whole economy. If countries produce a variety of products, they will be less likely to suffer from large demand shocks. Hence, more diverse economies will face fewer trade fluctuations and see smaller increases of unemployment if shocks occur to one industry. This also reduces the need for monetary policy stabilization, since any given shock has a small impact on the overall economy.

Sometimes further criteria are also given, but they are less important. These include "solidarity" as well as homogenous preferences across regions, for similar reasons as the condition of similar business cycles. 
    
So you can use these criteria to evaluate whether certain countries or areas should have the same currrency or not. All these criteria are definitely not fulfilled for the whole world, so there is a role for different currencies. An issue with the theory of OCAs is that it is unclear how much weight we should give to each criterium. So it could be unclear how to evaluate whether two countries who partially fulfill some of the criteria should have the same currency or not.