A lot of cyclists drive too, so surely with a reasonable amount of ease their car insurance could cover them when cycling too.
I wouldn't be against cyclists having some kind of insurance too if they weren't drivers though. It would have to be quite cheap though.
Perhaps the cycling proficiency test should be compulsory.
Cycle paths should be far improved though.
How about pedestrians having insurance?
How about none of that but designing safer streets and being 1000x stricter with dickheads behind the wheel of a motor vehicle?