the problem is that with isolation the kids can't go out for exercise at all whenever they are off school, so it's not a normal comparison
So your "yo-yo-ing" is only talking about isolation due to close contacts? something that only a minority of students were facing during the autumn term in any case, certainly there were some individual schools where that was high, but that is simply demonstrating that national approaches are mistaken. The schools in those areas were simply open when they should not have been.
With isolation of just some though, we get the situation of is numbers, the smaller amounts of harm to a million vs the larger amounts of harm to fifty thousand. We don't even have the evidence of that for the existing lockdowns of everyone else, let alone expecting it just for kids.
Mostly though it's clear that peoples description of yoyo-ing is not what I thought it was, and what they actually mean is isolating due to close contact in the school, not whole school moving to remote learning.
I'm not sure the evidence for 1 week in 1 week remote works btw, 7 days between infection isn't enough, better to go a bit further. Also general community spread is low enough that such schooling is viable, the kids will be meeting outside in any case, as I can't see any situation where community spread is low enough to not have everyone in lockdown, but high enough to require particular extra attention in schools.