Earlier quoted context omitted.
I think kids are likely to catch asymptomatic or extremely mild Covid annually. That’ll potentially be 4-5% of their educational time. Kids of wealthy families with parents with flexible jobs will be fine. Not every kid is in a home situation like that.
You have to look at both sides of the intervention, right? Like if isolating that kid doesn't prevent any further infections, then it isn't doing any good. If isolating them for 3 days prevents a couple other kids from getting infected, it's less clear. Using PCR tests to evaluate clearance doesn't make sense though, since they can be positive if there are fragments but no viable virus.
It's a cost and time issue. The cost of filtering snot, inoculating a culture dish of infectable cells with the filtered snot, waiting a couple of days for the cells to show signs of infection (cell swelling or bursting), and then running a PCR test on the cells in the culture dish. With high enough throughput you could probably do this for $50 or there about, and maybe three days, to verify whether they were technically still infected three days ago.