[my_username_is_]

This may be because I don't live in a "real city" (population 100k, US), but I see people biking with kids all the time (typically in some sort of cargo bike that has had seats added to it). The big threat while biking with kids (or without kids, for that matter) is from cars clipping you as they pass or pulling out in front of you. It's the cars that are the problem, not the bikes. Creating the infrastructure to allow people to bike safely will allow people to do what they're already doing more safely, and it will encourage more people to try it themselves.

[bkor]

IMO the problem is not the car, nor the bike. The problem is that they're sharing the same infrastructure. For new infrastructure I'd suggest also thinking about mopeds and quick electric bikes.