Just because it can be done well doesnt mean it isn't a shortcut around good writing for a LOT of these stories.
It hands the writer a blank cheque for exposition and worldbuilding because the main character needs to have everything explained to them or figure everything out and it excuses any form of set up as to the how and why the character is in this situation.
Australia has a mixed system.
Theres some nuance to this but essentially the government covers most things but you might wait a long time, especially for anything that isnt actively killing you. You don't get to pick your doctor, you get the treatments that are govt approved and you get shuffled out the door just as fast as humanly possible.
Private health insurance means you can choose your specialist, you have more of a say in your treatments and if your specialist says "If you want to go home tomorrow you can, but I'd like you to stay in for 3 days ideally" and you can if you want.