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
No, it's not a given. I've never heard anyone want that before