In BC, Canada, auto insurance is managed by the government. We have low insurance rates to begin with, and then we get a cheque in the mail at the end of the year if they collect more premiums than they pay out. (It's not a straight annual thing, of course. I don't know the details, but over the longer term it's how it works.)

It's kinda weird not having any sales pressure, too. They aren't at all light about upselling extra features. I only just found out that for ~$30/yr, I can add replacement car coverage to my plan. Over a lifetime, that's like $2K to never need to worry about a collision leaving you unable to drive for more than like a day to get a rental.

German here, the answer is no. Our public transit is crumbling left and right. Our health insurance too though. Serves us right for voting conservatives into power again and again for the last 30 years.

I have to imagine the tail wags the dog both ways in that scenario. Better public transport feeds into better public health outcomes, and nationalised healthcare (should) have a vested interest in reducing auto reliance for myriad reasons.