The government may have that incentive, but what about the individual doctors who are actually examining patients and diagnosing people? Do these employees truly share their employer's desire to cut costs?

I don't really believe that doctors are keeping people sick on purpose to keep demand for their profession high, but if that were going on, I don't think socialized healthcare would necessarily erase that incentive. There are plenty of government and private sector workers who try to preserve their own jobs to the detriment of the whole.