In the US, about 25% of health care costs go exclusively to administration. In countries with a national system, admin costs are about 10-15%. Also, in the US at each level of care (research, pharmacies, doctors, hospitals, insurance co's) a profit is added to the cost. This is greatly reduced in countries with a national system. Finally, the US gov't does not use its bargaining power to negotiate things like drug costs. Countries with national systems do.
Add all that up and it leads to what should have been an obvious fact from the beginning, i.e., a for-profit health care system is much more expensive than one run for the public good.