It is generally agreed that the system we have here in NZ is working.
It is very rare for anyone here over 65 to be homeless or in real poverty.
It helps that there is still relatively low inequality across the population despite decades of neoliberal policies where corporate power has eroded workers rights and incomes.
Look at countries where there is no welfare for the elderly and ask yourself would you want to live there?

Part of the problem has been that people do not have children as much as they once did and the population as a whole is aging.
Plus the fact that real wealth creation and trading surpluses have shifted from the western democracies to Asia.

I believe a basic universal pension can and does work because it does work well here in NZ.
Different countries and cultures will have unique challenges- the USA has the problem that it is in an economic war with China and USA has been dependent upon its exceptional privilege based on the petrodollar and that privilege is likely to be lost in coming decades- that is a wider problem than funding retirement and welfare though of course it does make such programs a real challenge.

Believing that 'markets will fix this' is naive at best and almost certain to result in massive suffering and trauma for millions of elderly.

Affordable housing is definitely a major part of the problem to be sure.
Here in New Zealand our current right wing neoliberal government has slashed social housing support and there are starting to be growing numbers of homeless.
If homelessness gets entrenched you are creating complex multigenerational problems. Markets alone do not fix these problems- what is needed are affordable housing programs and support.