I'd wonder how easily the results would be matched up.
If you get a positive, does the message suggest you confirm it with the PCR and give you a link to click on, for example?
What percentage of people know it's a good idea to confirm with a PCR-I suspect not as many as you would think. Several parents I've spoken to didn't know that, parents that are normally fairly on top of science advice.
And then add in those who won't bother for various reasons to confirm. Ones whose dc really hated doing the test, ones for whom they think isolating for 14 days is not too much of a problem, those who can't be bothered to go to a test site and don't realise you can order them online, those who have had contacts and know they already need to isolate for that time anyway.
I think if one of the dc (or me) was the only one I knew to get a positive LFD, then I'd probably retest. If there were known contacts then I'm not sure I'd bother. As with Piggy's school, if there's 12 positives in one group, the chance of all of them being false positives is tiny.
But I think with the LFDs the thing to look at is if the numbers of positives are increasing. If they're increasing, it's more likely to be increasing with infections than increasing with false positives.
Also I want to know what results in a false positive. It's a different matter if a false positive means an earlier infection, for example. If a false positive means that there was an earlier infection, then we would expect false positives to get fewer as we go along, assuming people don't retest after they've had a positive.
If it's contamination, or a problem on the test, then we'd expect similar numbers.
It's important to be looking at how the numbers change as much as absolute numbers becomes important.