I find bike paths more dangerous than roads, and given the choice will choose a well designed road over a bike path any time. Cars are predictable and stay in their lane. Cyclists on a trail are not, and do not. Trails attract casual cyclists, roller bladers, and pedestrians, that all act unpredictably. You don't have to worry on the road that an oncoming car will drift to your side of the road for no apparent reason. On a bike path, lane drifting is the norm. It's true that a collision with a fellow cyclist is likely to be far less serious than a collision with a car. But it is also far more likely. A busy cycle path on a nice day, with all kinds of riders going all different speeds and directions, is a hazard.
We have people who play with their bikes on a 6 lane divided road, they cross into the far left to turn left across 3 lanes of traffic and ride two or three to a lane.
I find it hard to believe a bake path is more dangerous than that.