But the elephant in the room is that if compulsory it means registration and number plates, otherwise it couldn't be policed. That on all bicycles is hardly acceptable and why almost everywhere it's been tried it's subsequently been dropped.
A more viable alternative is a compensation fund, financed by a levy on each bike sold. It could be run by a Cycle Insurance Bureau, just like the Motor Insurance Bureau covers claims when drivers aren't insured.
Our bike sales run at around 2.5 million a year so the levy would be small since bikes rarely cause a really costly accident.
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I am not at all convinced that number plates are necessary. At one time, yes, there was not the technology to do otherwise. Now, we could chip every bicycle. (Of course, there are arguments against doing that. Just identifying one option.)
It still has the same gross unfairness that MIB results in - those who pay having to pay again. (Not that the MIB shouldn't exist and I have no better idea as to how it could work and be funded.)
I suspect that if there were mandatory insurance, more people would pursue claims for things like scratches to cars, even when done by children. No idea what the number of settlements of claims in the UK currently runs at (whether through legal channels, or just person-to-person passing over a few fivers).