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I don't think it's unlikely that they're banned in inner cities at all,
In the intermediate term it'll be effectively banned by:
- higher insurrance rates and liability
- lack of parking
- cost to maintain old motorcars
Given the impact on infrastructure I think we'll see a lot of wide ranging changes--- just as we saw in the wake of the individual motorcar. Roads too will change. While the highway system might have started off for use by bicycles they clearly developed in the last century for automobiles. Once the critical mass in replacing the installed base is reached it should be a short way to banning them-- similar to the manner with which many places have banned horse driven cars. Self-driving cars will redefine road design in ways that preempt driving.
- higher insurrance rates and liability
I don't think it's unlikely that they're banned in inner cities at all, maybe it's a bit of a stretch for rural driving in the shorter term.
I'm also intrigued as to whether the 'roads are just for transportation' argument will come back to bite cyclists in the arse...