It does seem like it. However, there's the game theory problem/positive feedback loop where each parent who defects and drives their kid makes it more dangerous for all the other kids who are still walking; iterate a few times and everybody has defected and is worse off than before.
Perhaps it was culture, but the above loop only needs cheaper cars and more income, both things present in the 70s as the effects of WWII wore off.
Its far safer to walk than it was in 70s despite more parents driving their kids around but we still have kids walking less. The feedback loop is possible, but its not what is happening.
I think its linked to a general feeling of safety. I live in a village where people feel they know each other etc. and lots of kids walk to school. Kids in cities are statistically as safe, but the atmosphere is different.