It's not hard to make a list of "freedoms" we're mostly happy that people give up: the "freedom" to drive 100mph through school zones, the "freedom" to sell patent medicines with Pfizer branding on it, the "freedom" to set tire fires on our lawns. Those "freedoms" are respectively outweighed by the cost of collisions, of medical fraud, and of toxic and repulsive clouds of smoke.
When societies adopt single-payer health care systems, they're expressing a judgement that the "freedom" to take individual control over how to finance health care at the lowest possible price is outweighed by the cost to society of the uncertainty of health care costs.
And, setting aside principle for a moment, your health & well being is in fact one of the most important uncertainties in your life. You could be hit by a bus tomorrow, or stricken with a disease that outstrips your ability to pay for care. With the exception of a tiny, tiny fraction of people in society, nobody can truly provide an assurance of their ability to provide for their own care. So, to bring the principle back into the picture: if you're ideologically opposed to single-payer or socialized or mandated health insurance, it would seem that you must also support the idea that people who can't pay for their care must be denied care.
There's a wide variety of pragmatic objections to single-payer insurance, many of which are probably valid. But if we're going to bring "freedom" and "choice" into the picture --- ideology, in other words --- we should be clear about what the tradeoffs are.