Although some models would surely be better than mere qualitative [counter]arguments, Tyler Cowen, who teaches economics at George Mason University, put forward some counter-arguments, although his arguments are against a more specific proposal of Robin Hanson (another GMU economist) who proposed creating "Hero Hotels" where [young] people would get "variolated" with Covid-19. Some of Cowen's [counter]arguments (I'm skipping some):
Qualified medical personnel are remarkably scarce right now. I do not see how it is possible to oversee the variolation of more than a small number of individuals. [...]
The NBA has an amazing amount of money, on-staff doctors, the ability to afford tests, and so on. And with hundreds of millions or billions of dollars at stake they still won’t restart a crowdless, TV-only season. They could indeed run a “Heroes Hotel” for players who got infected from training and play, and yet they won’t. “Stadium and locker room as Heroes Hotel” is failing the market test. Similarly, colleges and universities have a lot at stake, but they are not rushing to volunteer their dorms for this purpose, even if it might boost their tuition revenue if it went as planned (which is not my prediction, to be clear).
Does small/marginal amounts of variolation do much good compared to simply a weaker lockdown enforcement for activities that involve the young disproportionately? Just tell the local police not to crack down on those soccer games out in the park (NB: I am not recommending this, rather it is the more practical version of [Hero Hotels]; both in my view are bad ideas.)
Society can only absorb a small number of very blunt messages from its leaders. You can’t have the President saying “this is terrible and you all must hide” and “we’re going to expose our young” and expect any kind of coherent response. People are already confused enough from mixed messages from leaders such as presidents and governors.
(Some of Cowen's later arguments are more into the realm of behavioral economics.)
Cowen is actually somewhat sympathetic to the idea of sorting who is (most) exposed to the risk, but he concludes by saying that
I don’t think Heroes Hotel, and accelerating the rate of deliberate, publicly-intended infection, is the way to a better solution.
It would be more interesting (of course) if these competing ideas/intuitions (Hanson's, Cowen's) were more formally modelled.
I suppose I could add that China did run fairly large centres when they quarantined everyone they thought were infected (though not infected on purpose), the so-called "Fangcang hospitals". There were up to 16 such facilities opened at one point in Wuhan, with about 10,000 people in them at the peak, but reportedly these have all be closed now.
Hanson doesn't seem to make any quantitative estimates how many "hero hotel" rooms would be needed (e.g. per capita) to achieve some concrete effect in reducing the economic downturn, although he does advance a scenario in relative population risk terms as:
For example, in a simulation where old and sick people are selected for isolation, while only the young and healthy are eligible for variolation, there are 40% fewer life years lost, compared to no variolation and random selection for isolation. Each variolation volunteer suffers only an additional 0.20% chance of death to save a random other person from a 6.5% chance.
Alas, he doesn't seem to (even) quantify the (relative) effects of variolation "on top" of non-random isolation of the old (which is a more plausible alternative than random isolation, which Hanson uses as the yardstick.)
I see Hanson has (also) written a reply/rebuttal to Cowen's points. I won't get too much into that here because Hanson e.g. says
If variolation cuts death rates by a factor of 5 (median estimate in this poll) [...]
Where the "poll" is a Twitter poll Hanson ran rather than some medical expert poll (at least). So the arguments seem based on rather dubious/uncertain parameters... which is what I suppose also precludes more serious research/publications on this proposal.