Your cycling fallacy is…
“Cyclists cause incidents and therefore should have insurance, like other road users.”
People on bicycles, although involved in a significant minority of incidents on the road (and pavements) are not a substantial threat either to themselves or others. The frequency of incidents involving people on cycles is – as with the number of motorcycle incidents – more linked to how vulnerable cyclists are compared to the average motor vehicle.
Requiring cyclists to hold insurance would make little difference (if any) to the volume or severity of road traffic incidents. Indeed, the only likely outcome of requiring insurance would be fewer people cycling: at the time of writing we're not aware of any country which has managed to implement such a scheme and police it.