although realistically you won’t face any consequences unless you do drive.
this is really the key point, i think, that makes gun control non-analogous to restrictions on vehicle use. there are essentially no restrictions on purchasing a car (other than owner registry, as you pointed out, which is something). if you want to purchase a car, take it home and put in your closet, the state has nothing to say to you.
the fact that enforcement of vehicle use restrictions is possible because cars are large, conspicuous and used on public roads while guns are none of those things also factors into how non-analogous these cases are.
In either case, there are plenty of deaths either by pure accident or poor storage (so it gets in the hands of a toddler or sandy hook type guy) where insurance would make sense.
does auto insurance reduce dangerous or reckless driving? maybe it does, but i'm not sure that it's obvious that it would. likewise, i'd think that your child not dying would be incentive enough for people with children to secure their guns (how many gun deaths are the result of young children playing with their parents' guns? i assume not many, but i don't know), but i admit that humans often do respond prompts pushing them into behaviors that were obviously in their interest even without the prompt.