Right. In essence, I think these details of the redistributive function are what make it Ponzi-like or sound.
On one end of the spectrum, you have personal and "defined contribution" saving and investment schemes: the individual carries a personal pool into their later years where they draw it down. How are differences between the contribution+performance and lifetime needs reconciled? Estates pass inheritances or individuals are bankrupt and we recursively ask ourselves what sort of system will cover their needs.
In the middle, you have what I think you want. An insurance pool redistributes the contributions, performance, and needs among a cohort. How are the aggregate assets and lifetime needs of the cohort reconciled? Contributions could be curtailed in response to excess accumulation or increased to cope with unexpected needs. Like any insurance scheme, the risk management has complexity around managing liquidity in the face of time-varying needs, contributions, and investment/economic performance.
But what skeptics see is an ugly reality unfolding further down that spectrum. Population growth and the long delay between contribution and withdrawal is (either naively or willfully) misinterpreted as excess accumulation. This is used to justify either insufficient contribution or "theft" of assets to fund other initiatives than the insurance pool. This leaves a hollowed out pension systems with defined benefits that cannot be satisfied with their meager holdings. As with a Ponzi scheme, they appear to work while the incoming contributions from an ever growing cohort are used to pay outgoing benefits to an earlier, smaller subset of participants. They collapse when the participation rate fails to grow fast enough to meet the ever growing needs of the aging cohort.