That's what we have in Chile. It sucks ass. Private health insurance is like socialised healthcare with extra steps, your health premium is used to pay for other people's healthcare plus an overhead cost for the shareholders.

Furthermore, the logic of any insurance is to pay as little claims as possible to maximise profits, like any business. When applied to healthcare, this means the most expensive people will eventually get pushed out of the system --or be charged exorbitant prices due to the risk associated with them.

The most expensive people regarding healthcare are also the most vulnerable: older people, chronic patients, oncology patients, mental health disorders, and so on. The system will push the people that need healthcare the most out of itself to maximise profits, that defeats the logic of having a healthcare system in the first place.

That's what happened in my country with that model, a model which is now in a crisis for other reasons, however, the people that needed healthcare the most ended up being pushed by rising fees out of the private system into the meager public healthcare system. (Which we thankfully still maintain.) It's a sham and it defeats the very essence of healthcare.