The same dynamics play out with pension schemes. Declining birth rates play havoc with proposals that rely on a large, young employed base who's work supports a small, retired set of pensioners.
My own perspective is that healthcare is extremely limited on the provider side. Professional organizations have been limiting the supply of doctors / doctor equivalents for decades. Not to minimize the work a family medicine or general practitioner puts in, but many important health services/early interventiona can be safely and reliably provided by a nurse practitioner or physicians assistant (what a horrible name) on a much larger and affordable scale then exists today.
It's a perverted cross between escrow and welfare in which the population basically pays their own way in the long run plus supports all the people who make their living by being "administrative overhead" along the way.