The other great thing about public transport is you don't have to "lug" / "chauffer" them at all after about 8 or so (what age makes sense depends on area and the kid of course). They can exercise some independence.
How much does it depend on where in the US you are?
The probability that any given child will be kidnapped or otherwise threatened by a stranger is minuscule compared to the chance that they will be abused, kidnapped, or killed by a family member.
That's sort of the point about low probability events though, it doesn't affect the average but it has a significant impact on the individual.