"government can negotiate even better rates"

Yes. Up to a point. It's true that in general, the government currently pays less than private insurers.

What's not clear is what happens if/when the government is the only one paying hospitals to keep their doors open. At the reduced rate, hospitals will have hard choices to make. Only about 20% of hospitals are for-profit. For the other 80%, less money coming in the door will result in changes of some kind. I can't imagine how hospitals can do that, and make things better for patients at the same time. Something's got to give.