You have the main point of the fundamental problem. They make money in three ways
1) You die before you draw more than you put in
2) You have a pyramid set up where more people join than are in retirement so more funds are being put in than drawn.
For these reasons pensions are very difficult, if not impossible to sustain. This is why the US at least largely shifted to the 401(k) / 403(b) type system so long ago that very few people young enough to be on Reddit have ever had the opportunity to participate in a pension.
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