Certainly privately owned ones skim a lot off the top to pay shareholders and bonuses, but the reality is that the cost of caregiving is almost entirely labor and rent, and those things do not benefit from efficiency gains, so the cost of service just goes up forever because of Baumol's cost disease.
Realistically the only way to stabilize the price of caregiving is to automate the hell out of it, like Japan is trying to do. It's a rather dystopian thought that the only way senior care won't bankrupt us is if we have robots do it all, but what can you do.
The Baumol effect is only one component and not the entire story. Those that run these services will extract as many profits as possible for themselves. When the robots will manage geriatric care, there is no reason to not continue exploiting the patients' wallets.
Labor, who pays a sizeable chunk of their income on rent... and rent, well is rent. Rent is only expensive when demand outstrips supply, and demand keeps being artificially constrained by existing property owners (of which boomers are a large chunk) not willing to take a hit on their property value. Seems like a self-inflicted problem.
Realistically the only way to stabilize the price of caregiving is to automate the hell out of it, like Japan is trying to do. It's a rather dystopian thought that the only way senior care won't bankrupt us is if we have robots do it all, but what can you do.