Logic vs. Emotion
Logic dictates that when two systems collide, the more powerful system wins. Creating two separate systems for bikes and cars is an idea favored by the motoring public, because "they win."
A separate system for cyclists, apart from the same roads used by cars, will of necessity be inferior and subordinate to the system used by cars. When one meets the other (which must happen on a two dimensional scheme, unless you want to invest millions in "bicycle bridges,") the cyclist will always have to yield right of way to motorists. Always.
Separating cyclists from motor traffic, from a cyclists' viewpoint, is based not on logic (see above,) but on emotion: the cyclist's alleged fear of traffic. This is a poor basis for any safe transportation system.
Separating cyclists from motor traffic, from a motorist's viewpoint,
is based on logic, as it should be: get the bikes off the street and I don't have to deal with them.
When logic and emotion collide, who will win?