> countries without that or with less generally have better outcomes at less cost.

This isn't necessarily a great metric, because almost all countries have better outcomes and all countries have lower per capita cost, whether their systems are public, private, or mixed. The US spends more public funds on healthcare than countries with universal socialized health care systems. The fact that we're also personally bankrupted after spending the same tax proportion on healthcare is just a bonus.

It's not specifically private healthcare or insurance that's the problem, it's the specific corruption of the people who own the healthcare industry and their legislators.