> As far as I know, the social security program in the US isn't actually structured in such a way that each person's SS taxes are going into an individual investment account under their own name (despite the "how much I've earned" statements which might seem to suggest this).

It's not structured that way, but you do need to 'earn credits' to establish eligibility for benefits, and the benefits are calculated with a formula based on the amount of your wages that were subject to social security tax; and the official name is old age insurance. It certainly feels like it's retirement insurance that you pay into while you're working, and get the benefits should you live long enough.