Health care in general has been solved by state sponsored medicine in most industrialized nations. And when it isn't solved by directly state sponsored medicine, it's solved by formally and informally regulated monopolies. In fact, US health care in the 1960s was made reasonable by the Blue Shield regulated monopoly.

The thing about unfettered private health is that it finds "profit centers" and pumps them ruthlessly. But the problem when scheme/scam gets reigned in (say out-of-plan doctors), another appears (out-of-plan ambulances) and there's no end to the situation. Only actual state sponsored health care can end this.