No it won't. Single payer healthcare in the US will be run by the Centers for Medicare and Medicaid Security (CMS). A wretched hive of scum and villainy.
An intensely bureaucratic, irrational and bloated system that will most likely keep most of bad points about American medicine. And add a couple new ones. You think the giant insurance companies are going to go away? Of course not. They will simply shed their skins and turn into 'third party' administrators of the 'single payer'. Exactly as they do now. It will be a giant shell game. Guess who is going to win and guess who's going to lose?