I think this compares apples and oranges. A better comparison would be public v. private hospitals. A public coverage option to the extent that it becomes pervasive will affect the incentives for technological progress because it will tend to affect the market generally. It will tend to drive down the reimbursements to private health care providers (not insurers) in a way that stifles the incentives for innovation and that rations care through indirect means (wait times and reimbursements based on some centralized notion of "quality").
There could be, I suppose, clinics and hospitals that refuse to accept government insurance or to conform to its limitations. To the extent that the public option - because it is artificially cheaper - becomes pervasive, most people won't have access to it. That is consistent with the experience in many "universal care" systems and, indeed, is not entirely different than what happens with education (at least in the absence of vouchers.)
But the problem is deeper than that. There cannot be innovation for a private sector of the market that is too small to support it. Education seems different in that regard. One of the constant themes in the left critique of market economics is a failure to see what will not happen when the market is constrained. That's happening here as well.
Another commenter, TosaVoter, asks the following question:
I’d like to ask him a question. It’s a false choice, but then Shark himself asked a similar question so I think it’s fair: If God himself appeared before you and said, before you get into Heaven, you must answer this question: which would be your greater priority – the private market system and the health of private insurance companies, or patients?
That's easy to answer. It would be the patients. The test of the market is whether it produces a better outcome than a nonmarket system would. But that question can't be answered by finding market outcomes we don't like and then demanding that the government fix it by fiat without hurting anything else. Economic reality has a tendency to get it the way.
This whole debate has been about whether to throw out the baby with the bathwater. I say no.