Retirement plans are already unsustainable, retirement age is raising everywhere in the world. UBI is basically a life-long retirement scheme, requiring at least 10x more resources.
Retirement schemes are currently funded with such creative approaches that Enron would be ashamed of. No stone left unturned: continuous refinancing with future taxes, securitization, implied zero default risk, assumptions of constantly growing economy, and more. Even then, US direct social security is 25% of all budgetary expenses, and with Medicare/Medicaid it is around 60%, much larger than anything else. Unsustainable means unsustainable.
That's a problem with America's dodgy retirement scheme, not retirement schemes in general. In Australia for instance, the government enforces mandatory saving for retirement, but neither the citizen nor the government are able to access the money before retirement: https://en.wikipedia.org/wiki/Superannuation_in_Australia. This means that peoples' retirements are actually funded by real savings, not by wealth transfer from younger workers, so it doesn't matter if the retired population significantly outnumbers the working population. Singapore has something similar: https://en.wikipedia.org/wiki/Central_Provident_Fund.
I too am in the Australian Super. This (what you write above) is mostly true except there are moments in our system, the defined benefits hole for federal employees which required the government to make a sovereign fund and the ever-present question: where are the workers, to make money, which the superannuation fund investment managers can then profit from, to pay out super?
I was totally shocked when I learned about how bad the US superannuation regulations are. Raiding funds. funds which invest in the company you work for as their main investment. Permitting early access to funds for things which might look neccessary but really underpin other systematic failures (cost of homes/equity, medical bills for non-terminal diseases)
Aussie workers with a US fund incur costs, because the US fund isn't recognized as a tax compliant super fund. And you get a long tail overhang of the US IRS looking at your income on return to Australia.