I get that a positive RT-PCR result doesn’t prove that replicating virus is present. It proves that its genetic material – the RNA – is present. If they're putting people into isolation based on the presence of RNA, replicating virus or not, I'd rather err on the side of caution than put the community at risk.
Even in high prevalence areas, are they really getting a quantity of positives per 10,000's of tests to call the risk of false positives a pervasive problem?
MIT did more than 156,000 tests on asymptomatic individuals through COVID Pass and had fewer than 90 positives. A positive-test rate of 0.05–0.06%, then a risk of a false positive test being astronomically lower again, it's worth it.
If someone tests positive, their first thought should not be "I bet it's a false positive" You've got a better chance at winning the lottery.