Yes, it is terrible the worst system imaginable, except for the system we have now.
How does a UHC system lower costs? I made some guesses. Does it matter?
The fact is that every civilized nation in the world has UHC, and they all pay less than we do. We can speculate on why that is, of course, and the answers might be of academic interest. The fact is that people those nations may have some complaints, but they don't want to adopt the non system that we "enjoy" here. The fact is that, whatever anecdotes you can find about doctors in one nation or another prescribing placebos for whatever reason, the outcomes are as good as or better than what we have in the US.
The only argument against UHC is that it is "socialism". Most nations do not have a real socialized medicine system. I understand that Spain does, and Spain still pays a lot less than we do.
Oh, and there is the convincing argument, which actually has been presented on this very forum, that all of the nations of the world are lying about how much health care is costing them.