>One even if funds go bust care of old people is basically done by young people chipping in and helping and that can go on.
If you mean "young people" in general, the fertility rate ensures they'll be less and less, and thus a heavier and heavier burdern to chip in for older people.
If you mean young people that are family, an increased (over 30%) number of old people won't have children or will have estranged children, and no help.
As for "AI and robots" don't bet on those either. It takes people to maintain an economy and an infrastructure that makes and deploys robots at any significant scale, and those will be scarce, and the demographic hit will make both productivity and consumption contract too. Societies increasingly can't even fix potholes and basic public services.
I was having a look after that at the current state of AI robots and they are coming along, eg. this is a figure robot folding towels https://x.com/minchoi/status/1961798845584613649
You don't have to extrapolate that much improvement for them to start having an impact and I imagine factories in China will churn them out like they do most other tech.
Whether or not there are enough young people does not matter.
The plan was to have fully funded pensions, bootstrapping them after the start. You cannot have infinite growth any case, as eventually we run out of space and resources. It must come to end at some decade.
However funding pensions full was never executed. It was too easy for politicians not to pass taxes, social benefit costs and such to do this, because boomers would have complained decades ago when they were still in the fullest earning potential.
So it does matter. Contracting economy, aging population, worse social dynamisc, political and institutional inertia, productivity drops, etc. Robots aren't going to offset but a tiny part of this.
And between payroll taxes and the fact that stocks, 401ks, etc depend on economic growth, things will turn real shitty...