It probably is cheaper.
I was told when I had my accident that the RCMP were insured by the Crown. It may mean "no insurance at all", or it may be a different insurance, because the RCMP isn't provincial, while ICBC is. I don't know. I actually don't believe you though.
I got rear-ended while stopped at a light. When I made mty claim, ICBC told me they'd have to talk to the guy in front of me before they could settle the claim - they wanted to know if he'd felt 2 impacts or just one (to determine if they were dealing with a single incident or two) Once he filed, all I had to do was pick up my cheque (the car was written off) I didn't have to fight them for anything.
From what I understand, most accidents are found to be 100% to one driver.
When I had the accident with the cop, ICBC gave me the royal run-around. The adjuster gave me all sorts of stories... which he back-tracked pretty quick when I took my Dad in with me.
I do agree with you on the monopoly thing... it's the same with phone service and banking and several other things. I don't know if I want it opened up to competition though - that just creates a different set of headaches.