I fully agree with the first 3 paragraphs.
On the fourth: Plenty of countries changed their healthcare systems for the better through political means. In fact, what other way would you propose?
On the fifth: Healthcare is always going to require insurance. Because people who are severely ill/injured aren't in a position to negotiate with providers on the basis of free market principles. And insurance will always require regulation and supervision because it otherwise invites all kinds of fraud, and not just the type (allegedly) committed by $UNH.
I think the $UNH case just illustrates the lack of such effective oversight. This is not impossible to fix. Plenty of countries seem to do a decent job of it.