Single Payer, Bargaining, and Prices Charged to the Uninsured

I’ve had this Ezra Klein post in the back of my mind for a few days:

One aspect of the uninsured crisis that often gets referenced, but rarely receives much focus, is the difference between what the insured and the uninsured pay for the same treatments. Insurance companies bargain down prices, and Medicare bargains down prices (though not on drugs), and so one way the providers eke out a bit of profit is charging higher prices to the uninsured — prices that are then picked up by taxpayers, or converted into debt and bankruptcy. A new study found that the uninsured paid, on average, 2.5 times what the insured pay, and three times what Medicare pays. So a procedure that hospitals charge Medicare $100 for would cost the uninsured $307. And they, of course, are exactly the group that can’t afford the mark-up.

There’s more in his post, and the article to which he links, but to me this raises a question… if insurance companies and Medicare are able to bargain prices down, wouldn’t a single payer system be able to do it even more? And nobody on the right seems to object to insurance companies doing this sort of bargaining – so why would it be a bad thing if an even larger entity did the bargaining?