I don't think there is a good way to study this, but one confounding variable I could see is that while kids in schools are fairly obviously great disease sprea

I don't think there is a good way to study this, but one confounding variable I could see is that while kids in schools are fairly obviously great disease spreading vectors in general, the fact that COVID is relatively contagious might have made school spread less of a factor. In other words, for diseases that don't spread as readily, school spread may be a more significant factor since less hospitable environments might not allow them to spread at all or only very slowly. Since COVID spreads well in all sorts of environments, whether or not school spread was controlled or not would matter less since it would still spread. And while parts of the US did have some pretty strict school closures for quite a while, other things being much less restricted might have meant the spread (or lack thereof) in schools didn't matter much since it was still spreading everywhere else. Whatever one might think of school closing as a policy, arguably the weirdest thing was that even in parts of the US that had more COVID restrictions in general, school closings were a uniquely restrictive outlier while everything else was relaxed. As was pointed out at the time, adults could go to packed bars far earlier than students could go to school. Even if school closings were worth it to control the spread, only closing schools seems like a questionable strategy.