There are a lot of confounding variables in these analyses. It’s going to take years to tease them apart, and we may never truly know for certain in some cases.
The point is not "is it wise to take precautions"; that's obvious. The point is we don't necessarily have great data on which precautions work better than others because they're largely all being put into effect at the same time.
We actually do, though, and it's preventing close contact of non-household members and preventing sharing enclosed spaces with non-household members for long periods of time.
People spread the virus before they even know they're sick, and a subset of sick people either need to go to work despite being sick, or they just don't care.
It's going to take time and years of research to tease out things like "did closing schools specifically help".