My compelling position on this debate is informed by ACTUAL first-hand experience of living in the U.S. and in Australia.

Healthcare insurance is a nightmare to navigate in the U.S. I witnessed friends having to spend hours haggling and pleading with insurance companies for coverage for very much needed knee replacements, post operative physiotherapy etc. And somehow, things still ended up being expensive! These people had better-than-average incomes (an optometrist who owned multiple downtown small buildings, and a home, all inherited, with no mortgages, and a psychotherapist with a specialized sort of practice and some inheritance wealth), so if you think you'll do well under privatization, you might want to reconsider that stance, given your resources and your tolerance for pain and frustration. Further, certain hospitals only accept certain insurance plans! So if you needed to go to hospital, you had to call aroud to see which one in your area accepts your insurance! Try navigating all of this with a sudden and painful kidney infection (I did, and it was a terrible and invonvenient experience despite my having a relatively good insurance plan from my employer). We aren't often aware how good we have it in comparison, here.

On the other hand, the Australians have an even better system than ours and it is less privatized. The average Australian can access good and affordable medical care with ease. If I were an Australian, I'd never leave.