It's possible to save pension by investing without pension funds. However the trick is that most pension funds are underfunded and run like a Ponzi, thus constantly need larger and larger group of young people to fund them. If and when this system collapses is going to hurt the government and that's why the encounrage to keep the Ponzi going.
The whole concept of "retirement" where old people are allowed to relax and be supported by young people, compared to the old days when people just worked until they died, requires enough surplus productivity from young people to look after old people as well as themselves.
If the population pyramid inverts and there are too few young people, the whole concept of "retirement" becomes unsustainable, unless AI advances enough to make up the lost productivity.
Pensions are just a way of formalizing the obligation to old people, but they are not themselves the root source of the problem.
Setting aside that 'too few young people' is by definition when there's a problem, thus making it a tautology, there's a lot we can do by changing our views of what retirement means.
Retirement should not mean a life of air travel and cruises, achieved by pension savings.
Retirement should not mean continuing to live in your 2,500 sq. ft. ranch house in the suburbs with only car access.
John Maynard Keynes famously predicted we would be working 15 hours a week due because of increasing productivity. Where did all that productivity go?
If it's because we believed we needed ('deserved') more, then change those beliefs. If it's because of the concentration of wealth into the 0.01% then AI productivity improvements won't fix things.
The AI-mongers sell the false and unsustainable promise that AI will magically solve things so people don't need to change their habits.
Yet we can achieve a lot of savings by building more compact areas to live which don't require a car, and by building mass transit with the needs of the elderly in mind (no steps, low-frequency lines which run through neighborhoods, for those with limited mobility, etc.)
We can save money and get better health outcomes with a tried-and-true single-payer health care system done in every other developed country (eg, "Medicare For All".)
That can all be done now.
Yet we aren't. Because it's easier, and more profitable to those with money, to ignore the festering problem, with the fig leaf of 'AI' or some other future technology, and let someone else deal with it,
Also in many cases we must accept the fact that people die. And some times keeping them alive is too costly or take too much labour. I admit it is horrible realisation, but I think inevitable one.