One alternative, if you're not fond of the idea of banning cars altogether, is to do the same thing that you see a lot over here. Basically any street people live on is a dead end, or almost a dead end. Taking a shortcut through a residential street basically doesn't happen.
Take the neighborhood I live in for example, It's all one-directional traffic with tight corners and speed bumps. It has more exiting streets than entering streets. The end result being a decided lack of traffic, while still being able to get a car to your front door when you need it.
Kids can play in the streets safely enough, There's a couple cars an hour most of the day and the few cars that do pass are going slow enough to not hit any kids. The most dangerous time of day is all the parents getting their kid out of school by car.
You sometimes see a commercial vehicle trying out a new shortcut. People only think that to be a good idea once. Going around is faster than going through in any case.
Carless doesn't have to be an absolute. It's a gradient from six lane highways through your neighborhood on one side, and no cars at all on the other. A balance needs to be found.