Your concerns are extremely valid, but it is not _that_ bad in many places in America. I relocated my family specifically so that my kids could have a walkable community to live in, and since then (about five years), we've had no issues with them getting to schools, parks, the library, friends' houses, and downtown shops on their own.

That said, we live in the inner district of a small city that was settled in the mid 19th century, so it has a street grid, alleys, uninterrupted sidewalks, etc.... everything that makes a place as safe as possible in this day and age for kids to get around without getting hit by a car. (One exception being dedicated biking infrastructure, which would be awesome.)

At what age did you start letting your kids run errands or walk to school by themselves?