The cyclists around here travel the bike lanes at their peril. The car drivers are so bad around here that they have run over several cyclists and the bike lanes for the most go unused except by the ones that illegally drive on them.
Bicycles, and human-powered vehicles of all kinds, are very specialized forms of transportation and while they fill a niche for recreation and limited commuting, they are by no means a serious factor in moving large numbers of people, and that only over short distances.
Where there is a mix of pedestrians and cyclists, the separate paths make some kind of sense, but to mix human-powered cyclists with motorized traffic is mixing oil and water.
Militant bikers are wrong of course. It is also wrong to deny bikers designated road space just because they are not using a car. What would some do if say, gas got impossibly high? Or if more than one child needed to go in opposite directions?