Really, in the long run, it was intended to save taxpayers and the states money.... The reason I say this is that seat belt laws were around in most states long before car/health insurance were required; if someone was in an accident who didn't have insurance, they were less likely to sustain major injuries if they were wearing their seatbelt. It's the state (and eventually the taxpayers) who end up paying for uninsured people, so seatbelt laws were a way to reduce costs.
Now, I think once you're an adult you should choose whether you want to be safe or not, but small children definitely need the safety restraints....It's unfortunate that the people who don't put seat belts on themselves, also tend not to make their children wear them. (There are exceptions of course.)