You still put a bunch of money into it on the promise that after retirement you will have income, and that promise is broken when you renounce your citizenship. Also, Social Security is closer to real pensions than you think, they're just different from the theoretical concept of a pension that isn't actually used outside of the Post Office.
You're using vague words like "promise". "Hope" would be more accurate. Someone can correct me, but if Congress passes a law tomorrow saying they're not going to pay social security after 2025, that is probably allowed. The only "promise" is to people who are currently retired.
Furthermore, if you renounce your citizenship, it is you who are choosing not to get this benefit. It is a defined benefit for citizens, and you are choosing not to be one.
As for similarity to pensions: Far from it. When the government has an excess (i.e. total SS taxes collected is greater than payouts for a given year), they are not allowed to hold it or invest it. Pensions are/were always invested, or at least held.
> Furthermore, if you renounce your citizenship, it is you who are choosing not to get this benefit. It is a defined benefit for citizens
Individuals who renounce their US citizenship (or were never citizens) are still eligible to receive SS benefits; SS actually has very little to do with citizenship.