I've researched UHC from other countries before and invariably you will find that that system is in trouble, normally due to money issues. There was even a country where the UHC was failing but the private health insurance companies were working great. Sorry can't remember which country this was.
What needs to be done is for a group to get together and research every country that has UHC and list all the pro's and con's that is currently happening with those countries. Find out which is the most prevalent con's and which is the most prevalent pro's.
When this is done then IF people still want a UHC try and figure out a way to prevent the con's.
Take the best of each countries system and improve upon them.