Socialized healthcare systems often have room for a private sector, so you can have both.

You can also go to other doctors in a socialized one, if their treatment (style) does not fit your cause.

Also, in my experience there's lots of choice in most socialized health care systems.

I had a gastroscopy in Austria, the Doctor asked me if I'd like a general anesthesia or rather a local, nerve blocker - mostly to avoid the gag reflex.

He said that it may not be as pleasant without the anesthesia, but I still opted for it and am really glad I did. While it really was not pleasant, I was up and going again in about half an hour.

Nah... that has more to do with how medicine is practiced versus how it's paid for. I'd bet you'd have troubling finding any doctor willing to sedate for an endoscopy in that country.

It's just "how it's done". Just like the US has it's own unique methods that seem odd to Europe.

Oh, you can do it privately instead. Costs $500 or so, but there's as much choice as the market allows for. My description was how it's normally done in the public system.

Do you have other reasons, perchance?