What if I stopped giving my money to insurance companies?

I just read about how the two insurance excutives are getting millions in bonus money even thought the government bailed them out. I think that is super wrong. It actually makes me sick that those kind of people are around, just trying to make a buck and not care who they hurt financially.

My question is. If I owned my vechicle and got liability insurance only (because its required by law) and took the other money that I would have spent on full coverage and stuck it in an account. And then used that money if I got in an accident. Would that really benefit me, or do I really need to keep paying these companies for there services?