Mr. Walter Williams has an interesting take on insurance and laws like the one requiring you wear a seat belt.[1] In short, he lumps these in with socialism, and in a very real way he is right. The only sense in which these are justifiable is that in which people who are injured from their own recklessness become a burden on the public. But they would not be a burden on the public if the government were not taking care of them, that is, if socialism were not in place.
The exception to this is private insurance. Given private health and car insurance, you still become a burden on a subset of the public if you are reckless. That being said, private insurance also has a mechanism to deal with this. We charge higher premiums to smokers, and you could write in an exemption for seat belts, that is, you would not be covered if not wearing a seat belt. So I think that in the end, private insurance would compensate for the lack of social welfare laws, with much the same effect, if the socialism were scaled back.
[1] http://www.townhall.com/columnists/walterwilliams/ww20050615.shtml