A competent bike helmet costs little, but not nothing; maybe $20 to start, and a little extra weight, and it messes up your hair a bit, takes seconds to put on if already adjusted and maybe a minute otherwise. May remove a bit of vision, but only vertically up.

A competent car helmet is probably a motorcycle helmet, which is more like $100 to start, but it impacts hearing, reduces vision in all directions, is a significant weight, usually doesn't adjust much for sizing, takes longer to put on (especially if you wear eyeglasses).

A bike helmet in a car would likely be more trouble than anything, it would interfere with the headrests and probably increase neck injuries.