Free Health Care isn't Free

I really don't like the idea of the U.S. adopting any sort of Universal Health Care System. I think it is both presumptuous and arrogant of us to believe that we could enact a health care system like the U.K. or Canadian systems without any of the inherent problems and inabilities of those systems.
Even the the best model for universal healthcare, the U.S. Military medical system, would be an unlikely model to use. The military healtchare operates under ideal circumstances, but is still unable and inadequate to take to task the needs of its clients (please google Walter Reed for references, this is a blog, and I can't be bothered with facts, references or whatnot). Most military members are healthy (being as everyone is medically screened before acceptance) most workout daily, do not smoke, and eat fast food in moderation. Why then, is military medicine not better than privatized healthcare?
I am in the military (as a dependent). Under ideal circumstances, I waited 40 minutes for my doctor's appointment today. Spent 15 seconds with the doctor and was referred to a specialist. But, my visit was free. Why then, do I feel like I was robbed an hour of my life?