I was peripherally involved with an Ontario plan for public car insurance back in the '80s when Bob Rae was thinking about it. I made myself unpopular at the company by suggesting that the government just bought the BC software, a handful of 2nd hand IBM mainframes to run it on and did the minimum initial fixes...different post codes and stuff like that. Started it up and let it run, bugs and all, although I suspect it might have been a fairly rugged software suite. But when you double the number of rows in a database bad things can happen ( I wonder if it was something like an old IBM file system rather than, say, DB2, at the time.
Fixed it up later if ever for bilingualism and other more complex stuff.
One argument against public insurance nowadays is that the US owned insurance companies would sue the province for billions of loss of business. I don't think they'd get far with that as NAFTA does not apply to sub national jurisdictions... but it is a convenient argument for government. Another one would be, I bet, the assorted changes in Human rights legislation over the last 30 years that the cost of mass firings when the private companies went out of business would somehow fall on the government...could be... I have heard this one when discussing getting rid of the LCBO as well