The US is about thirty times larger than Poland and much of it was developed after the wide adoption of automobiles. Few children live within a mile of their school here, and of the ones that do, there are often not walkable routes to get there. Many roads in the US have no sidewalk and are intended only for vehicle traffic.
I am one of the few parents that trusts their own kids to walk a short distance to school by themselves. I have received a few comments from other parents implying negligence for trusting my kids.
I have doubts that it's busy roads that changed this behaviour.
Is that really true? 80% of Americans live within large metro areas rather than rural areas.
Look for the percentage who actually live in the cities, vs. the metro areas.
And when I lived in the Denver suburbs, my brother attended a couple of county schools. The junior high was at least a couple of miles away, the high school more like five. Do not underestimate American sprawl.