They like companies with some kind of moat that makes it hard to unseat them. Basically, companies where there is no alternative for the consumer. That way, they can inflict abuse but know there will be nowhere to run.
There are two different ways to achieve this. Monopoly and regulation. Hospitals have both government granted locational monopoly and tons of regulations that make it impossible to compete.
Private equity is the symptom, not the disease.
Until we get at the disease, new monsters will be born with different name filling the same ecological niche. It's economic natural selection played out in the environment we created.