Yes the US does spend more. Canadian healthcare still isn't free. By the standard of contribution vs cost of treatment, insurance can likewise be claimed to be "free" to the individual who needs it.
I just provided that link as a source, not that I necessarily agree with it. So the question is do you think that the claim that the amount spent on healthcare is equivalent to 2/3rds of income tax is incorrect?
I know the rest of what I say is going to ruffle some feathers.
So healthcare is not free.
Road and bridges aren't free.
The military isn't free.
How are these being paid?
Through force.
Through the aggressive coercion of taxation and violence of the state.
BTW, I detest the use of the moniker "government services". A waiter at a restaurant serves me. My internet provider serves me. My interaction with them is voluntary and solicited by me. The government is quite the opposite. The government violates the non-aggression principle. My internet provider does not.
The dichotomy of government or corporations is a false one for a couple of reasons. Corporations are legal entities granted protection by the state. The actions of corporations within a state system exist because a state allows it. Without the state, and the legal framework surrounding its corporate laws, the liability of the corporation cannot be limited, and the influence of corporate power over the state is nonexistent. Almost always when people complain about corporations "screwing people", it's when they are abusing some aspect of the state. So when "corporations screw you over", I would argue it is because the state is complicit in the act.
More to the topic on hand, could a state-controlled system be more effective than what currently exists in the United States? Quite possibly. First we should ask why is it that American medical costs are increasing so dramatically, beyond normal inflation? Why is it that medical care has become expensive, whereas other aspects of the economy have generally become cheaper (such as electronics)? I would argue a few reasons, most of which relates to government intervention through subsidies and protectionism. With both state funded medicare/medicaid as well as employer funded insurance (which is heavily subsidized by the government), the consumer/patient is far less likely to discriminate with healthcare based on cost. When someone else is paying for a person's care, there's every incentive for that person to spend a lot of money on treatments or drugs that, while much more expensive, may only be marginally more effective, and there's every incentive for healthcare institutions to charge for them. Employers have trouble fighting this largely due to privacy regarding one's medical care/history. The state run institutions (medicare/medicaid) are largely designed to cater to specific voting blocks (the elderly and poor respectively) and as such are explicitly designed to pay for such care. They do not have the same economic requirements of a business, but rather need to use these premium medical benefits and lower deductibles as incentives for voting a certain way (as it is neither party wishes to challenge the situation, so it happens regardless of who gets into office). Not to leave out the corporations, they too get in on the action through lobbying efforts (of Big Pharma) to have state funded medical care to purchase name brand products over generics (link). In that same note, they have lobbied to restrict imports of cheaper generics, forcing people to buy them online illegally or pay exorbitant prices. The IP/patent monopolies enjoyed by Big Pharma further contribute in this way. Past lobbying efforts on the part of trade and professional associations, like the AMA also contribute to rising costs, who have worked to limit the amount of professional medical practitioners through licensing under the guise of patient safety. Another consideration is that Americans in general make poorer lifestyle choices than other first world nations, obesity being the most obvious. This drives up the need for medical care, and subsequently the cost as well. The result is that the United States has a mixture of corporate dominated health care along with state funded healthcare (medicare/medicaid). It leaves much to be desired, and I certainly would not defend it.
From this perspective a state-controlled system could potentially be seen to be an improvement if it adequately dealt with some of the abuse that takes place. But I wouldn't count on it considering how embedded government subsidized cronyism is. It's just more likely to be perpetuated. With that being said, I should add I'm sympathetic towards healthcare. For example, I think healthcare would be a much better expenditure of tax money than the military. However, that does not mean that I would support it.
If the government were not using tax income (force/violence) to provide the service, and the service was paid for through voluntary payment of customers, I may support it, but then that wouldn't be the action of a government, but of a business. So I just simply ask "If such a system is so good, why should it need to be forced upon its customers?" Because, if a service is good and desired by people, it needn't be implemented by force.
On top of this, when you have state healthcare, the reason for health laws becomes more transparent. Taxing the obese, taxing smokers, taxing lifestyle choices all become necessary unless the burden is transferred to those who do not make poor life choices. Further to that point, you get the young paying more than they would otherwise to subsidize the elderly. You get men subsidizing services they would never have a requirement for (e.g. maternity care). All through force.
So when you dismissively say "Of course it's not 'free'." To me, you're just arguing my point.
Beyond this, I'm not really interested in further consequentialist arguments if it the arguments being made are violating my ethical principles.