check out Australia's healthcare system as a middle ground then. I've lived in the UK (free, single-payer, government-run) and Australia's, and I prefer Australia's because it has a mix of both government and market.
The basic principle is that the Australian Federal Government subsidises healthcare by a fixed amount for each procedure. So iirc, it was AUD$45 for a visit to the GP. That's enough for some GP practices to be able to offer a free service (referred to as "bulk billed" because they only billed the government). Obviously those services become popular, so to get a free appointment you have to wait a while. Or, you can pay a bit yourself to get an appointment with a doctor who charges more than the government rate and are therefore less in demand.
In Australia I could usually get an appointment next day if I paid $25-50 or so. In the UK it was usually a 1-2 week wait, but free.
This goes for everything (except dental care for some reason, I don't know what's up with that). So an X-Ray costs $200, or nothing if you can wait until next week. And so on.
Health insurance covers the additional costs, and I paid $25/month for a plan that meant if anything serious happened I'd be liable for the first $250. And it also gave me dental cover, so I could claim some (but not all) of my dental care from my health insurance - a net gain for me most years.
The NZ system is similar. GPs are subsidised (your primary health provider) but hospitals are run by the government and are free. The unfortunate thing is you have to go through the GP to get a referral to the Hospital (unless you go into A&E).
The other interesting system that NZ has is something called ACC which also pays for rehabilitation and loss of income when someone has an accident. If you are paralysed and can no longer work then ACC will pay you something like 80% of your income until you manage to find another job. That could be for the rest of your life.
The basic principle is that the Australian Federal Government subsidises healthcare by a fixed amount for each procedure. So iirc, it was AUD$45 for a visit to the GP. That's enough for some GP practices to be able to offer a free service (referred to as "bulk billed" because they only billed the government). Obviously those services become popular, so to get a free appointment you have to wait a while. Or, you can pay a bit yourself to get an appointment with a doctor who charges more than the government rate and are therefore less in demand.
In Australia I could usually get an appointment next day if I paid $25-50 or so. In the UK it was usually a 1-2 week wait, but free.
This goes for everything (except dental care for some reason, I don't know what's up with that). So an X-Ray costs $200, or nothing if you can wait until next week. And so on.
Health insurance covers the additional costs, and I paid $25/month for a plan that meant if anything serious happened I'd be liable for the first $250. And it also gave me dental cover, so I could claim some (but not all) of my dental care from my health insurance - a net gain for me most years.