It would be in the "public interest" to install seat belts on toilets as well, because someone might fall off and hit their head on the pointy corner of the bathroom sink that needs a protective rubber coating.
People fall down stairs everyday, so why not pass a law outlawing any structure that requires someone to step up?
People choke on food all the time, so should we pass a law requiring food to only be served in liquid form, but not hot liquid because you might get burned and not cold liquid because you may get "ice-cream headache"?
How about beds? They should be required to have rails around the side because people fall out of bed all the time.
You see where I'm going with this (hopefully). Once you allow the government to tell you what you have to do for "your safety" in public, they will soon be able to tell you what you can do for "your safety" in private as well.
With that being said, I will now put my federally mandated helmet back on my head, so that if I fall I will not sustain life-threatening injuries requiring millions of tax-dollars to remain in a vegetative state.
I think that you are missing the scale of car accidents. All of your mock examples are highly unlikely events. Over 100 Americans die in car accidents every day. We need to minimize the governement money spent on health care for the far greater number who survive. Just to rile the conservatives, I'll point out that their " I don't want the government protecting me from my own stupidity" argument also implies support for the repeal of laws prohibiting drug use.