Such a system would be run by the government which is answerable to the voters who are the people who need the health care. Decisions would be made with a goal of keeping patients happy and healthy, not making someone a profit. We do, through our taxes. Before complaining that you already pay enough taxes, keep in mind that you and your employer will no longer have to pay for private insurance. Look across the border to Canada.
Physicians have their own private practices.
Patients see the physicians of their choice. All fees as negotiated by the government, and all bills are paid by the government. This alone decreases physicians' overhead and gives them more time to actually practice medicine. Plus, since every citizen is eligible, doctors do not have to worry about what is or is not covered by which plan. As HMOs have told us so often, it is cheaper to prevent a disease than to treat it, so this is another potential source for savings.