Being largely for-profit is part of the problem with healthcare in the United States, but plenty of other countries have privatized healthcare that works, Japan being the first that comes to mind.
The difference being that, in the US, the long-term dysfunction of our political system has allowed the regulatory framework for healthcare to be built to service its own industry, rather than the needs of individual citizens or society at large.
As one example, regional hospitals used to band together in groups to bargain collectively when purchasing supplies. This arrangement was formalized, legislated, and then warped, so that rather than the hospitals controlling the organization, it was instead controlled by the suppliers, driving the cost to the patient up, rather than down.
There is no easy solution here, without first fixing our broken political system, and I see no evidence of that happening.