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.