Anything infrastructure should not be left in the hands of for profit organisations, and health care is among the list of things that are infrastructure.
That does not necessarily mean that such things should be provided for free, many mass transit companies for example are owned by government entities and charge fare and there's nothing wrong with that. But they should be operated with an eye towards getting a result that is not just 'stockpile as much money as possible'. If that means the company only covers its cost as it serves millions of people a day? Well, that is not failure state for infrastructure.
It only needs to cover its construction and maintenance costs over the course of its life, and that only if the people decide that it's not part of their contract for the purchase of government services and thus covered under taxes.
That does not necessarily mean that such things should be provided for free, many mass transit companies for example are owned by government entities and charge fare and there's nothing wrong with that. But they should be operated with an eye towards getting a result that is not just 'stockpile as much money as possible'. If that means the company only covers its cost as it serves millions of people a day? Well, that is not failure state for infrastructure.
It only needs to cover its construction and maintenance costs over the course of its life, and that only if the people decide that it's not part of their contract for the purchase of government services and thus covered under taxes.