Then why do we pay more for health care per capita than people who live in countries with nationalized health care?
Because the United States does not ration care. Other nations employing a socialized form of healthcare, by necessity, must ration care because for something like one's health, the demand will always be greater than the supply.
An excess of demand over supply causes high prices, not low prices. So it canot be (and demonstrably is not) a
shortage of care in more civilized countries that makes healthcare cheaper.
As for "rationing", any form of "rationing" which in no way restricts the access of any individual to goods or services is not in fact "rationing". Perhaps you should think of a new word for it, such as "unrationing" or "antirationing".