Or just have schools change their hours as needed.

Time changes are just a hack to make every business change their effective office hours back when the sign on the door - and coordination - mattered. Today brick and mortar is way less relevant. Way more people are working from home or going to work at random hours. The time change doesn't affect going to grocery store or restaurants or the gym. It's basically just schools, banks, and the DMV.

Why not have a given entity change its hours through the year, if the relation to the sun actually matters?

(And no, I don't buy that there needs to be time coordination between schools, since they are all already slightly different anyway. Different kids have different after school programs different days. Different parents are already going to work different hours. There's no way to coordinate for everyone to be happy, ever.)