Careful, "for-profit" healthcare has a lot of government controls on it. Single payer is only obvious after you add a lot of controls to the market.

See https://www.youtube.com/watch?v=8q71hrwUcu0 and the more complete https://www.youtube.com/watch?v=rWlk9HreE7U.

He explains how regulation eventually results in a centrally planned setup that is less efficient than what used to happen.