The issue with schools is the problem is allowed to develop and then gets out of control in the same school.
Its not dealt with straight away.
You don't have to test in every school. You focus on schools where its become apparent there is an issue. So you need several teams to do that and go to the schools with an ongoing issue.
So for example about 6 weeks ago I think there were 40 odd schools that had postive cases recorded in my area (I believe its currently 20).
You target each one with a problem. You don't over stretch your resources. You don't create work in schools where there isn't an issue.
If you target, the theory is that you gradually get on top of the problem properly, rather than half arsed bubble closures. Nor testing kids who don't really need to be tested.
Blanket testing is just a dumb idea because of the resource and personel issue.
This is still whack a mole, but its fine tuning the whack a mole and improving it.