You are asserting that children would be engaging in higher risk activities than attending school for the same duration as they would be attending school, which which you’re almost certainly wrong about (not least because of course the majority are learning on Zoom during that time). It’s more likely that the reason spread is lower in schools is because children themselves are less likely to contract COVID and also less likely to transmit COVID- not because schools themselves are inherently low risk. This applies in non-school settings as well, of course. On the contrary, you’d be hard pressed to find a higher risk activity.
With minor adjustments you can eliminate contact between classes, that would essentially create a bubble around each class making transmission very unlikely. As soon as you let them run loose they're coming into contact with many other people.
I've been saying this for a long time, and I think it's pretty straight forward. People don't spread COVID by coming in contact with the same people every day, it's when a new potentially infected person gets added to the mix that transmission becomes much more likely. The most obvious case in the frum world is weddings, we see people going to shul, work, and stores every day with little transmission. As soon as you add weddings to the mix it starts spreading like crazy.
The same will apply to students, when they're hanging out on the streets they come in contact with new people every day making transmission much more likely.