There's a short-term problem of society becoming "top-heavy", where there might not be enough young to pay for the continued care of the old. But in the long run this seems like a win. I wonder what impact it might have on climate projections.
Its an active and intentional decision not to do so. Unless society collapses and the knowledge of how modern mass production works to produce so much plenty evaporates it will continue to take a tiny percentage of the whole population to provide the resources needed to survive to the rest.
We should be expecting a technological singularity before 2100, not some dystopia where all wealth evaporates and the only people with money left are under 30s who get to work 80 hours a week farming rice for grandma.
Unless we have such a population implosion that we can no longer produce food or run our factories, then we don't need to "pay for" anything. We can simply decide to distribute the resources necessary for the care of the old.
The real cost of everything is the labor required to produce it, not the dollar value it receives in a market place. I don't think anyone is talking about a complete collapse in the labor pool.
Retirement financing in general relies on future economic growth for future cashflow. That said, you don't necessarily need a growing population to make it work. If the population declines 15%, but the average worker's productivity goes up 20% during that time, you still come out ahead.
The core unit of the economy is not cash, it's value. Saving roughly corresponds to avoiding consumption and preserving value; in a very basic economy, this would take the form of e.g. preserving grain in a granary rather than eating it all. People or government savings systems that save for retirement are then able to consume the value they saved when they retire; they don't require any value transfer from the working population.
Whether you measure the overage in units of lifetime granaries, or running annual surpluses, is primarily an accounting choice.
As a practical matter, it's impossible for one farmer to save up enough food to span their entire retirement. Storage is an expense, and food goes bad eventually. The concept of a retirement is only possible in a society that transacts value regularly.
Society doesn’t reward you based on the value you produce but based on how much fictional currency you have. This could be entirely granted to you for example in a a lottery and you never produced anything of value.
Think of a reverse Corona virus that only kills the young. Retirees have lots of money but the shops and factories are closed.
The only solutions are technology or rationing care.
Edit: I've replied mostly along the lines of the financial costs, but the human service component is by far the largest part of it, that's the main resource consumed.
The source of the panic is the 'exponential growth forever' dingbats being confronted by a reality they don't like.
Without the young, the house of cards collapses.
Advancements in existing technology just aren’t going to be enough at the timeline we’re looking at. Political change is another non-starter because it just won’t happen on a global scale. Then there’s the fact that for the vast majority of people alive today, the Earth’s condition in 50 or 100 years is rightly not even on their radar.