It's a very simple logic really. Lots of people think like you until they need something because they get unemployed, sick, have an accident.... It's basic insurance math; forcing everyone to participate mitigates the problems of adverse selection.
What if I ask you to consider which principles you would select for the basic structure of society, without any knowledge of what position you would end up having in that society. Without knowing your ethnicity, social status, gender, health and intellect. If you select principles impartially and rationally, most people select for a social security net, where the fortunate make the life of the unfortunate a bit less cumbersome. It's not just a pure waste of money for most wealthy either. It's quite inconvenient to watch people starve to death. It's also severely reducing the quality of life if you have to hide behind a fence because you could get stabbed for carrying a bit of money with you.
Prior to social insurance, the elderly used to be an age group with an especially high rate of poverty (which suggests the average doesn't or cannot save enough before becoming to old to work). Indirectly, their working-age children are beneficiaries of the system as well because the elderly no longer have to move in with them.
It's unlikely to go away, because the US had lived through times without it and chose to leave these dark ages behind. If you don't want that, there are still plenty of choices; Haiti, Sierra Leone, Uganda, Afghanistan, to name a few. It seems though, these places aren't particularly nice destinations. I'll leave it as an open question if lack of social security benefits plays any role here. You'd have to give up US citizenship though, because you must file a US federal tax return and pay US taxes on your worldwide income no matter where you live.