[Retric]

If a society is not able to pay for 'perfect healthcare' then it will not pay for 'perfect healthcare' under any system.

However, as your reduce the cost of providing healthcare with single payer systems you increase society's ability to provide high quality healthcare. Remember, if a doctor sees 1000 people a month then you can detect fraud by randomly sampling 20 cases. However, if 10 companies each need to check for fraud they may investigate 10 cases each, but with 10 X 10 that's still more effort. Further, they are each going to try and cost shift to the others, which is an expensive zero sum game.

[icebraining]

However, if 10 companies each need to check for fraud they may investigate 10 cases each, but with 10 X 10 that's still more effort.

Or they'll coordinate to avoid the duplication, usually by having some kind of industry society/non-profit that does the checking.