I hear this a lot about social security in the US as well, that it will fail. I would characterize it as degrading instead of failing. If the workforce declines there will be fewer payers into social security or pensions, then folks paying into social security will have to pay more, recipients will get fewer benefits, or the government will print money
It is not a "Ponzi scheme" at all, rubbish. The pension system is not an investment theme. Currently working people provide for current pensioners. No "investing" involved. That, in the light of a shift in age distribution, this works better when the economy and productivity grow is orthogonal, the pension system payments are not for economic growth but directly for current pensioners.
Unless you find aliens or a time machine to shift goods and also services through time, always and everywhere the currently working take care of the current pensioners. There is nothing "Ponzi" about it, that is the universe.
People who pay now do not pay for their future pension, they pay for the current pensioners. What is transmitted to the future - when they become pensioners - is not what they pay now, it is merely information. That information is then taken into account when the then living and working working people pay the pensions of the then pensioners. The information about how much somebody contributed in the past is taken into consideration to see how much a share of the overall pie everyone gets, but the pie itself always is created in the present by whoever works now.
Which also makes the headlines a little silly that claim that because in the future there will be more of an imbalance between nr. of people working and those getting a pension something needs to be changed now. It makes no sense: The current payments into the system immediately go to the current pensioners. If there are less paying and/or more receiving the funds that can and is always balanced at whatever the current time is. There is no need to do anything now when the current payments are enough to pay the current pensioners. If next year there is an imbalance they adjust what the payments (in and out) are at that time. It makes no sense to change payments now when the problem is not right now.
Any finance-based scheme cannot undo the universe (except, aliens helping out or time machine). "Private" funds change nothing of the underlaying truth that current pensioners live from what current workers produce in both goods an services. It only changes who is responsible: More winners and losers (and then "it's your own fault, why did you not buy stocks - the right stocks too of course") with the finance based system, with one huge winner the financial industry.
This also applies to private retirement investments. My comfort in retirement is contingent on the economy, and hence, the stock market, growing. If the 'ponzi scheme' of limitless growth collapses, I'm not going to be any better off than the pensioner.
I'm not sure that any public pension systems in any way satisfy the definition of a Ponzi scheme. While public pension systems may be flawed, in no way are they fraudulent or otherwise non-transparent at the very least in democratic regimes.