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The major problem here is that people who don't have health insurance will still need healthcare, except it's going to be much more expensive (due to putting it off until it's life-threatening, which always jacks the price up), and since they can't pay for it, the cost has to be offloaded onto the "responsible" people who "chose" to have insurance. Allowing people to choose whether or not to have health insurance is only superficially increasing freedom of choice - when you look deeper, you see that you're not allowing the injured to make a choice they want, and you're forcing everyone who pays anything to pay for the health care of other people, whether they want to or not.
You might as well lessen that burden that gets spread around. If you create a system where people automatically pay a certain amount for healthcare (no matter what that healthcare might be), and can't opt out, you create an incentive to actually use it when it's most cost-effective, which could potentially save money. And if you're saving money, you're actually improving the freedom of the participants - not only are you giving them the choice of seeking healthcare or not, you're also giving them a greater degree of economic freedom.
What would be
better is if this were implemented through a graduated tax, and when you checked into a hospital, you didn't have to pay at all. The system would just assume you'd paid your share in tax money, and you'd get treated. Hospitals get a budget each year paid out of those taxes. Maybe institute a check for tax delinquency or convictions for tax fraud*, but no actual monetary transactions should really be necessary. Leaving the insurance industry and the healthcare industry as profit-driven enterprises converts the "you cannot opt out" part of the idea into a way of shackling you to a machine that has every interest in charging you, and no interest in treating you.
EDIT: I'd actually be against this, because it undermines the whole point, but it might be necessary to sell it to people who believe that there's a moral aspect to who "ought" to pay