This is a fundamental misunderstanding of how these funds work.
The goal is not to pay people with the money from new people paying into the pot. They invest the money and then the pot grows and that money is used to pay out. When the pot is not growing enough - whether because investments aren’t doing well enough, or you designed a you designed an bad system where people can withdraw from it for too long, or any other many possible issues - then yes you functionally end up dipping into the money given by new people, but this is not how it was designed to be used.
You are acting like this is a one-to-one system where you just put money in, then you get money out later, and all of the money given out is 100% the money that people put in in the first place with no intention of growing that money or finding a sustainable way of disseminating it long-term.
Mismanagement/poorly built systems are not the same as Ponzi schemes. Unless you think, I don’t know, US Social Security is also a Ponzi scheme?
When did I ever say the problem goes away? I am saying it is not a Ponzi scheme. You were saying it is a Ponzi scheme. Don’t move the goalposts here.