That incentivizes gaming the system by getting multiple tests, though, and hoping one will be lucky to be the newest batch. If you can centralise test assignme

That incentivizes gaming the system by getting multiple tests, though, and hoping one will be lucky to be the newest batch. If you can centralise test assignment enough to eliminate that, you can do something smarter, like prioritising health workers, at-risk demographics and those who are already asymptomatic. Assign any remaining capacity quasi-randomly to get the best possible statistical data for your epidemiologists: if your systems are that overwhelmed it's far too late for contact tracing to be useful, but the data scientists may learn something. Having inefficient assignment of test resources is a problem inherent to privatised distributed healthcare that doesn't just go away if you solve the financial side with Obamacare or the like.