What I think really matters for most people is not to find out whether they have covid or not, but whether they are infectious or not. I'd really like to see research (any at all!) into how effective different test methods are at predicting infectiousness and am disappointed that this never seems to get addressed. Because who cares if you're asymptomatic but your viral load is low and you're unlikely to infect others…
We don't have a labor and cost effective test for this, and we require the test to be done in a BSL-3 facility.
So what remains is that we need to solve public health problems with tests that produce only correlates of infectiousness. Those correlates will be necessarily imperfect, but they're all that we have to craft policy around.
The perfect home test which only detects infectious virus doesn't exist.
And I'd just like to see more published studies which actually cultured virus rather than using PCR as a proxy for infectious virus, but even that is hard to get. So many lazy scientific studies out there conflating PCR positive with virus, but there's a lot more researchers who can do PCR than researchers than have access+funding to a BSL-3 lab.