Isn’t the school solution, as done in many countries, to reopen them (with usual restrictions—15 per class, 2m, maybe 2 grades/day, maybe masks in classrooms) and then, if infection rates rise after a month, ratchet down the degree of openness? (Or if they don’t, ratchet it up)?
German schools generally reopened in early May, with those restrictions (so most kids had 2 days of in-person per week), and were ready to shut down again if rates rose. Rates fell, so some restrictions were dropped — ie in early June they decided masks no longer needed in class
This type of “modulation” policy has worked well in Europe. France has had to ratchet back some openings, as has at least one German city. But there have been many more ratcheting-forwards. You monitor and contact-trace, and adjust degrees of openness weekly
In countries where schools were open in May and June, it turned out that schools are not sources of infection — not at all. Outbreaks have been traced to meat plants, religious services, housing estates and I think occasionally to parties. But not to schools