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.