I agree with the first part of what you said but not the second. This is Singapore, i see joggers, pedestrains with pets and cyclists cycling abreast on all this "Cycling Paths" all the time and wherever i go so cycling on the roads are actually safer.
It's easier for parties to stop or give way to one another on the paths because of the slower speeds than on the roads.
Survival chances from crashes on the paths are also much higher than from a motorised vehicle crash. Sustained damages from path accidents also likely to be much lower.
Safety on the paths is far better even with reckless riders. As long as one uses brains, eyes, loud voice and fast braking fingers, accidents on paths can be averted.