This assertion you keep making that the tests don’t work.
I’ve not done any tests throughout this thing, I always resented the idea of doing them tbh.
But when I wasn’t looking MrsL ordered some lateral flow tests.
She was feeling really rough the week before Christmas and at times was quite breathless going up stairs. She didn’t tell me that last bit last week and I didn’t think it was Covid but on Christmas Day her taste and smell went funny so she took a test. Lit up like a Christmas tree, ironically. She did a second test and it did the same. I tested myself and that was negative - which I was a bit surprised by but I’ve not had any symptoms.
Boxing Day I tested our boy (lateral flow testing a 4 year old - 2 stars, would not recommend) and he was negative. I tested him again yesterday, and myself, and they were both negative again. MrsL tested herself again yesterday and it was positive again but the line was noticeably fainter and took longer to appear. Given the worst seems to be over for her that makes sense and I’m hoping in a couple of days she’ll test negative so we can do some family stuff.
Point being, do the tests work? All I can sensibly say from the above is the results I’ve seen have been consistent - the same person, who was experiencing symptoms, tested positive multiple times. The people who tested negative and who had no symptoms did so consistently too.
PCR we’ve spoken about before and the general wisdom there seems to be that you need to be careful about how many cycles you do to avoid false positives.
TL;DR - if by “don’t work” you mean they’re not 100% reliable then I’d suggest that is simultaneously true and not a sensible definition. That would apply to any test in the history of testing. But the lateral flow tests I’ve done gave consistent results and the PCR ones are generally thought to be more reliable by experts in the field if you do them right.