It would take healthcare decisions further away from the doctor/patient relationship. There would be a disincentive for the brightest people to even pursue a career as a physician because the government would restrict their compensation- guaranteed insurance but not guaranteed access to actual health care.
There is a reason why increasing numbers of physicians are either leaving practice altogether or joining large cooperatives to survive and why many have stopped taking medicare patients- government setting compensation and heaping more and more regulation and paperwork on them with no real benefit.
How much time do primary care physicians now send filling out arcane documentation versus providing patient care now? Under total government control you can double it and double the number of useless bureaucrats administering it. Right now, thanks to government interference, the average U.S. doctor spends 16.6 percent of his or her working hours on non-patient-related paperwork, time that might otherwise be spent caring for patients. And the more time doctors spend on such bureaucratic tasks, the unhappier they are about having chosen medicine as a career.