I'm ususally on the side of private enterprise; but I have to say that the BC auto insurance (ICBC)works very well. Premiums are reasonable, unless you rack up a bunch of driving points or have several accidents where you were deemed at fault, and seem to be less than equivalent insurance rates in the private sector in (say) Alberta. For my son, who now has about 8 years driving experience, his rates are more reasonable than would be the case under private ins. ICBCs claims reporting, damage assessments, and ease of getting your vehicle fixed are all good. I really have no complaint with them at all.
There is a fear of reporting minor accidents under private ins that doesn't apply under the ICBC rules, particularily things like "hit and run" where you are not at fault.
ICBC is run as a separate business and makes a profit (assuming the accouting is accurate!!). I do object to their involvement in areas that are not insurance related (such as buying commercial real estate under the previous NDP govt) but they are, I think, pretty much out of that now.
Overall, I rate them highly.