A Boring Dystopia

These people live in high cost care facilities on the taxpayer's dime for 10-20 years?

First, yes. Presumably they worked a full life and contributed to the taxes, it's their dime. Second, these people?

They cost 10-20K a month, or 120-200K a year

No they don't. That's what they cost in the exploitative private for profit system.

The demand for healthcare resources is simple vast out supplies care that is available, especially as the population ages. Hence in 'affordable' healthcare systems you are still undeserved and it's still expensive.

That's true, but not an issue of cost. It results in expensive private care, but the issue itself is the lack is labor, not that each patient costs $20k/month.

That's compiled by the fact healthcare workers, while in demand, and often getting good pay, burn out rapidly due to the demands of the job.

That's another real problem, but it's again irrelevant. It exists regardless of how socialized or privatized the system is...

Now we can keep people alive on machines for decades

Is that what you think happens in elderly care? Every patient receives terminal care for decades?

There are only so many beds, and so many staff that can work in these facilities.

You can fix that by better planning your economy, encourage students to pursue nursing and guarantee them jobs when they graduate.

Whatever the case, there are loads of "alternatives" to dropping them off at homeless shelters we can explore. Holy moly.