Sure, but in my experience, people never attribute high insurance costs to the underlying risks being high, rather they blame that on the insurance companies and then vote for people who promise to “do something about it“.

I’m sure there is brand damage from people hearing that a particular car is frequently stolen, because having your car stolen as a pain. I am skeptical the analysis reaches deeper than this first level tho.

I don't think high insurance costs would result in brand damage as such. But it absolutely would result in reduced sales and/or reduced resale value, because sufficiently many people comparing which car to buy will look at the insurance cost for each particular car they are comparing as part of that decision.