Sigh. So you're taking an absolutist position against insurance? How quaint. If you're doing business with the govt, certain insurance requirements must be met. It's the same for many kinds of licensed activities. If you drive, you must, by law, have insurance. ( I know- you'll circle back around the the old saw of "States Rights")
All of those kinds of insurance cover benefits that each of us may never use, but they're included as part of the package, often by law.
If your argument about paying for other's mistakes held water at all, we'd see insurance providers objecting to the contraception provisions of the new law, but we don't, because they realize it will save them and us money when we look past the ends of our noses.
I realize that in Libertopia, hospitals would refuse to treat people who can't afford to pay, that child welfare would be of no concern, that the aged & infirm would be on their own to survive. But it'll never be that way in this country, so we have to make rational rather than emotional choices in the realm of the possible. Within that framework, contraception is cheaper than welfare, and shared risk is better than individual risk.
Regardless of the positions of delusional moralistic libertarian poseurs, the American people have decided that we take care of our own, of each other, rather than just ourselves, and that we all benefit from that in ways direct & indirect, whether you can comprehend it or not. If the world really worked the way you think it should, rather than the way it does, then there would be no need for govt to implement any number of requirements on citizens.