Keeping retired people alive requires devoting some proportion of current economic output to their welfare. Whether that proportion is paid from private savings, public savings, or current taxation ultimately doesn't change the fact that it comes out of current production. You can't save (nice) food, health workers, winter heating, etc.

So the real fight is what proportion of current output goes to old people. Private schemes try to ensure wealthy old people get the biggest slice. Public schemes are more vote driven. It doesn't make them Ponzi schemes.