I agree. Certainly while in public (e.g. public roads).
That said, I want to say that got proposed in the 90s and somehow the NRA not only defeated it at the federal level, but got congress to ban states from doing it. I could have just imagined that tho.
EDIT: https://sclawreview.org/article/gun-insurance-mandates-and-the-second-amendment/ (summary: there's a couple of laws [one state; one local], that will probably get SCOTUS review eventually, but are on the books for now; it's questionable whether insurance will cut down gun violence.)
I'd expect guns to be at least as regulated as vehicles, but I guess vehicles don't have their own amendment.