I believe it's appropriate for children to assume such a burden. By such time, the adult children are probably in their 60s and have the financial resources to do so. Medicaid, Medicare and Social Security can help ease the financial costs.
I have to admit that if all parents knew up front that someday their kids would be choosing their parents' care, then most parents would cultivate a much more thoughtful approach to the job.
However there might be gaps in the logic. If the parents are financially unable to support themselves in their "golden years", then they probably weren't much better off in their 60s. Why then would we assume that their children could do so? Does that also include an assumption that the children are employed and able to support their parents from their income? Will the adult children (supporting their parents) spend all their salary & savings on their parents because their own children will someday support them?
Seems to me that we'd need some sort of optimal family worker:beneficiary ratio to determine whether the aging parent could count on the kid's support. Things might work out quite well when four or five adult children's wages are supporting an aging parent. The system might not work so well with one or two workers. Gee, maybe Social Security & Medicare have more ideas about that...
Besides, and not to sound morbid, but the "burden" of caring for aging parents in their 80s or 90s probably won't be more than 10 years (if not less).
I've been getting a heckuva tutorial in that area. I don't know why you used "quotes" around the word burden, but IMO it's a psychological and financial minefield for the adult children even if the parent has been ready (both psychologically and financially) for it.
My grandfather lived for over 14 years in a care facility, and I suspect that Grandma (while she was alive) was covering for him before that. The effort of managing Gramp's finances and checking on his care consumed a large part of my father's time, energy, and focus-- to say nothing of hundreds of thousands of frequent-flyer miles. It was a horrific burden even though Gramps had the assets and was generally in good health.
Today I'm facing the same burden with my father. He's at most two years into his Alzeimer's diagnosis. I hear you about the "probably", but statistics are cold comfort in this case.
This seems to be the traditional "Asian" model. Yet many young Asians in the U.S. are resistent to the idea that their parents will move in with them, even though there are certainly some advantages (in-home childcare, help with cooking and cleaning around the house, etc...)
I was unhappy enough with my upbringing that I'd never want my parents raising my kids. As I got to know my parents-in-law, I arrived at the same conclusion.