LFDs are decent for telling you if you're infectious _right now_ - they're much worse than PCRs for telling you if you have covid at all.
Disclaimer: I'm a software engineer, do not take medical advice from me. My partner is a biochemist and I regularly chat with a couple of council covid-response officers, and the above is the explanation I've had from them when I've asked.
If only we had some guidance and solid communication from public health experts that you could conceivably trust..
Like the grandparent, I know several people that have all of the covid symptoms, but tested negative early on. These people just go about their day because they think they have some other cold, then stop testing until their symptoms go away. I would probably do the same.
You drive into a parking lot, they hand you a test, you self-swab and give it back to them.
There is other testing available - this is just the county-provided testing. It’s well run.
Anecdotal: I was in my 3rd of 4th day of symptoms before I finally came up positive on antigen (at home and at testing sites; the test appeared to be the exact same). PCR showed it from day 0 but the results lag quite a bit especially right now in the US (it took 7-10 days for me to get the PCR back in early Jan).