The issue is that: 1) Road design - many/most cities do not have adequate road engineering to deal with bikes 2) Driver training - Road drivers in the US aren't trained to deal with non-car traffic 3) Weak Bike traffic law enforcement - I don't think that bike negligence is a key cause of accidents but I do agree that police enforcement of traffic laws on cyclists is lax.
So I disagree with the notion that bike traffic needs to have a separate roadway from urban traffic. I think there are plenty of good examples where a sharing system works.