That’s because the current insurance billing system is so complex and corrupt they are willing to accept Big Brother rather than continue to deal with it.
When you think ‘single payer’, think of the English family that was denied the right to bring their dying child to the US for alternative therapy. Once any State controls your access to health care, they control you.
We've tried single payer in the US. It's called the VA. The VA’s problems are exactly what you'd expect them to be. There are dedicated people, but not all of them are, and until recently you couldn't get rid of those who weren't (they were often ‘promoted’). Further, the system is a bureaucratic mess, with too many administrators and too few people getting the job done.