I think a lot of this simply depends on the distance between home and school (or other places kids need to go to) – so it's the difference between a compact city and sprawling suburbs.
Where I live (central Europe), the density of public elementary schools in cities is high, so kids walk there alone. The density of secondary schools is lower, so most kids use bicycles or trams / buses.
Interestingly, there are a few private elementary schools (usually english speaking) for children of expats, where cars queue up in the morning, while parents drop off their children. I've never seen this at public schools. I believe this is because there are only a handful of those schools, so they are further apart – and maybe also because the parents (growing up in the US or UK) are already conditioned that this is a normal thing to do.
Hundreds of 7 year old kids elementary are taking subway to go to school in my neighbourhood here in Tokyo. What you see is an American solution to an American problem.
To be fair, I saw the same in Canada as well, so I understand USA isn’t alone.
Having grown up and gone to school exclusively in the USA I always thought it was crazy how many parents preferred to drive their kids to school instead of having them take the bus. By high school I would guess that less than half of kids actually got to school by bus despite them all being part of the bus pickup network.