I'm willing to bet that there have been more superspreader events caused by PCR false negatives than by people who just want to disregard COVID.

PCR tests give people a sense of confidence. "Oh, this is probably just a seasonal cold".

The correct answer is "Isolate yourself if you're feeling unwell", not go to CVS and buy a PCR so you can take a photo of your Probably Not Sick Pass™️

The problem is that we now have a country full of hypochondriacs, so if we tell them "sorry there's no good way to detect your COVID without a hospital visit and a blood test" you'll just make them go insane because they'll believe they need to isolate for ~forever.

"but what about asymptomatic people" -- yep, another problem. There isn't a good solution.