When I moved to BC, my rate didn't change by much. But the rest of the experience got worse. For starters you had to go into an office for everything. In my case, it took a few times to get it right. They screwed up my license and insurance twice - things like name, address, etc. (In one case a field in their database was blank that a future agent said shouldn't have been possible not to populate... go figure).
Next they gave me incorrect information. They tried to tell me I had to buy an extra add-on for my liability coverage to carry over when driving in the US - which is dead wrong if you actually read the policy. I got into a 40-minute argument that wound up being me vs. every single employee in the office (they all wandered over to see what was going on). In the end we all called ICBC-central together - it took two escalations to finally get someone who knew what they were talking about who could authoritatively confirm I was correct and all the agents in the office were wrong. They were all stunned; the one I was dealing with said "Wow, I've been selling that package to everybody who comes in and nearly none of them need it!"
Years later I tried to make a comprehensive claim for ~$7k worth of damage related to a freak weather event. The ICBC-central agent said "don't even bother to file a claim, it won't be covered". Some time later I was chatting with my old Ontario broker who said it was a no-brainer and would have been 100% covered under my old plan. (In retrospect I should have sent in the claim anyway and put up a fight... but I just didn't have the time - was doing lucrative consulting, and it made more financial sense to spend the time on billable hours than wasting it on that).
Over the years they've made many more mistakes and generally drive me nuts. At least compared to the two different companies I used for insurance during the years I spent in Ontario. Again anecdotally, most of my neighbours haven't any good things to say about them either.
One silver lining of the pandemic is it finally forced ICBC to put a process in place for doing renewals over a combination of phone and email. Still not as convenient as in Ontario, but at least it's an improvement.
I still fail to understand why BC thinks they need their own government-run insurance provider. This is a solved problem in the rest of the world.