Growing up in former USSR, I, along with other kids, used a bike to get around and for pleasure and have always stayed on the sidewalk (I don't think there were any laws about bikes).
From experience, I feel there's very little chance of injuring anyone, and even if it does happen - it is likely to be much less frequent and much less serious than what we observe with the bikes sharing the road with the cars. On rare occasions (rural locations) where there was no sidewalk - you'd ride towards oncoming traffic, same as what common sense recommends for pedestrians - so that you can see the cars and can avoid them if situation calls for it. That's probably illegal in US, since it appears that bikes here are somehow deemed more like motor vehicles and not pedestrians.
To conclude - I think the status quo is misguided (originally wrote stupid) and dangerous and traffic laws oughtta be changed to put soft squishy humans on two wheels on the sidewalks.