Which Is Better: Lots of Cheap, Lousy COVID-19 Tests or a Few Really Good Tests?

Which is better: a highly accurate PCR test for the coronavirus or a cheap strip test that’s not especially accurate at low virus loads? Alex Tabarrok compares the two, but his comparison has lots of words and stuff and you might not bother reading it. So I’d like to present you with a simplified version:
PCR test: You take the test, and a week later you get the results. In the meantime you’ve been infecting everyone nearby. Conclusion: it’s pretty useless.
Cheap strip test: It can’t be any worse, can it?
Believe it or not, this is actually a fairly good summary. For something a little more official, here’s a chart from a recent paper that compares testing regimes. The pink bars are similar to what you get with a PCR test, while the gray bars represent a less accurate test:
If reporting delays are the same, the accurate test is always better. But if, say, the accurate test takes a week to return results then it won’t be as good as a cheaper test that returns results in one or two days. Note that this chart is based on a model, and in real life the cheap test won’t perform as well as the gray bars suggest. But it will still do better than the expensive test. The cheap strip test may not always work, but you can easily test yourself every day and there’s a good chance that if you’re infectious you’ll find out within 15 minutes.
So why not cover the country with cheap strip tests? Because they don’t meet the FDA’s minimum accuracy requirements, that’s why. Perhaps that deserves a second look?