You directly implied that the difference between the damage that bicyclists and cars cause when they collide with things was small enough that bicyclists and drivers should follow exactly the same rules.
However if someone does not follow the rules then the fines need to be vastly greater for cars.
You don't need to be Einstein to understand: E = m/2*v^2
A good start would be to place all the burden of liability on the driver with the heavier vehicle (maybe have a 20% difference in which it is split 50:50).
The free market could then sort out insurance premiums.
