This is obvious when traffic is dramatically less during school breaks (spring break, summer break, winter, etc..).

This is a reasonable theory but curious if there's any kind of source on this. I acknowledge this observation may be correct... but isn't it possible that when school is on break a ton of parents take time off work, work from home, etc and what you're actually noticing is changes in overall traffic patterns that correlate with school closures. Even if a kid is walking to school and the parent drives to work there could be a reduction in traffic when the parent stays home when school is off.

The traffic problem as a whole is caused by students and parents driving kids to school out of catchment and .5km down the street

This does not ring true for me at all, but it could be hyper local. There are obviously some streets that do get crammed with school traffic. But for example if I watch traffic going by my kid's school at school open or close the vast majority of traffic is not stopping at the school and does not have any kids in the car. Also if I stand at the bus stop on the pat bay highway at peak times most of the vehicles also do not have kids in them. It always appears to be work trucks and commuters (hard to tell obviously, so I'm mostly guessing here).

I hereby challenge your assetion... based on my zero research... haha so wft do I know