I'd often seen kids on the tram in Melbourne. Rarely on their own though, almost always in groups. In Wellington, you'd see them occasionally too in the mornings. They had dedicated school buses (city buses with the "School" sign on the front), but if kids were running late and missed their bus, you'd often see them on regular public transport.

One of the big problems is the lack of public transport in the US. Even with cities with good transit, the minimum age for kids on buses/trains is usually 12 (wasn't there an article on HN earlier about a New York man who's kids rode the bus in a group of three and how social services said he couldn't do that any more until one of them turned 13? I can't seem to find it now..)

Crime is more perception then a real issue. You're always most likely to be a victim of a crime by a family member at home. Actual child abductions are more hollywood and rarely real life. When it does happens, it's usually someone who knows the child via family.

I feel like this is yet another problem that could be solved via real transit and which will just be made worse by self-driving cars.