If kids have to be released to their parents and are no longer turned out en masse like they used to be, that will absolutely cause traffic and could very well be the root cause of traffic that exceeds the designed capacity of the school pickup circles.

When I was growing up kids within a mile of the school would walk themselves to school and back home with very few exceptions, often starting with first graders. But even a half mile is a long enough distance that many busy parents in the suburbs would choose to drive it rather than walk it four times a day.