There are so many other situations where people can accidentally cause property damage that don't require insurance. Its just the cars have a very high risk of causing huge amounts of damage very easily.
Why? If I get sick, I need to go bankrupt if I don't have an insurance, but if I run a stop sign on a bicycle, government should pay for medical bill?
This would make more sense in countries that have universal healthcare. USA isn't one of those.
If 2 cyclists crash in to each other they will cause minimal property damage
Additionally, I imagine it would be easier to get (and require) bicyclists to carry catastrophic insurance, since carrying a license would at least go some way towards demonstrating safe behavior. By carrying such insurance, both cyclists and surviving family would be protected from at least some of the financial burdens of accidents.
So, yes on two counts: Incentive for safer cycling and easier access to (and possibly mandated) financial protection from accidents.
It's very hard for a cyclist to hit and run
Example:
https://patch.com/california/san-francisco/pedestrians-hospi...
No, it's not a given. I've never heard anyone want that before