It's a ponzi scheme structurally and independent of demographics, this is tautologically true given the definitions of how these systems work and what Ponzi scheme means. Ponzi schemes don't only become so when they go deep into the red, they are Ponzis right from day one if they work by paying out early investors from the fees paid by later investors.

Giving up in this context means switching to a better system, not doing nothing. It's a really bad habit of political debate to assume that if the government provides a service, only the government can provide that service and anyone who criticizes their bad provisioning is therefore arguing for no service to exist at all (and therefore that they must be inhumane and evil). It's just a cheap and nasty debating tactic that you should avoid. "Giving up" means simply for all pension and social insurance to be managed by the private sector. Governments could maybe mandate you buy a policy, and they'd still regulate the private investment funds, but that'd be the limit of their involvement.

The advantage is that governments are much better at enforcing rules on companies than their own departments. There are lots of rules governing how investment capital is managed if you're in the private sector, but if government run pension funds were companies the management would all have been put in jail decades ago, and the Justice Department would be crowing about how it had protected vulnerable citizens from them. Keeping capital savings and management in the private sector (which is good at it) and rule enforcement in the government (which is good at it) would result in a fairer and more trustworthy system over the long run.

NASI is the National Academy of Social Insurance, which doesn't mean their results are wrong but does mean you'd need to pay very close attention to what they're doing in these surveys.

For example, they list reasons their respondents give for supporting social security and the first is "I know that I will be receiving benefits when I retire", but the point of the story we're commenting on is that they don't know that. They've been told that, and it might be true, but on the current trajectory it's not currently going to be true. If the NASI told them that social security was unsustainable, that their money being paid in wasn't being saved for them and they might well have fewer benefits than they expect or that seem fair, would they still agree?

If that’s true, then they should allow people to opt out. There’d be nothing to worry about.

I know you don't know me personally, but I don't want it. Living off of my children's labors feels deeply icky to me unless they offer their support willingly, especially when they're at the time in life that they most need to be investing in themselves and I've already had the opportunity to do that.