Except they can't overcharge because the government controls their main source of income. They'd be obligated to follow market rate or risk losing access to those government dollars. The only reason some hospitals and other medical facilities occasionally don't accept Medicare is that they can rely on other sources to make up for the loss. Once single payer happens, they are kind of shit out of luck.So instead of overcharging people because they have insurance to pay for everything, the government will be the one overcharged.