Most places I've seen, yes in the US, have bike paths, and houses are typically in a separate area from main thoroughfares. Why wouldn't a kid bike to a friend's house, or a local park?
The issue is just don't care, it seems. :(
I've never been in a place where I had to take a "busy main road" to get around locally. Cross it sometimes, sure, which can be done at a light. This sort of highlights the problem. Over-protectiveness, by examining the worst that can happen, and the worst scenario.
Despite that, I've avoided bad accidents and generally felt pretty safe, but only because I survived long enough to develop an acute intuition for when drivers are about to do something stupid/illegal/dangerous. Previous and contemporaneous experience driving a car on the same streets was also very important. I would not trust these streets with my daughter's safety on a bike, and I honestly won't trust her to read the idiots' minds until she has some experience doing so from inside a heavy steel cage.
Riding within neighborhoods like the one I live in now is a different question, though some people do drive quite fast through here, and the size of the typical modern car makes clearances and sight-lines rather tight. I do see a lot of older kids out on their own walking, often to and from school, which I think is great.
A lot of the people espousing the whole free range parenting stuff never actually walk around and understand what the pedestrian experience is like. If they did, they'd be strongly advocating for better road design and pedestrian paths. But you rarely see the two groups intersect.
Since moving here I've effectively stopped riding because of the drivers.
