Which, currently, at least half of the population can't afford. Would we really like to have half of our workforce easily disabled by illness?
Instead of providing health insurance as a benefit, the employer would simply increase the employee's salary; the employee would then use the money to purchase health insurance (or, if he so desires, something else).
Lower prices are not equivalent to greater efficiency.
The problem here is that you are focusing only on one particular part of the economy--the sector encompassed by the product that the government is providing. However, one must remember that acts in one particular sector of the economy have effects that might reach other sectors. To be concrete: when society produces more of one particular good or service, it must produce less of some other good or service, because its resources are limited. However, there is no way to know beforehand how much of each good or service is optimal. The free market remedies this problem through the mechanism of prices. A rise in prices is a signal to increase production; a fall in prices, conversely, is a signal to reduce it.
This mechanism fails, however, when the government intervenes--whether by controlling the prices themselves, or by taking over production. In either case, it becomes impossible to reliably determine the appropriate quantities of production. In some instances, too little of society's resources might be devoted to the product in question, the consequences of which are obvious. On the other hand, too much of society's resources might be used up, in which case
other parts of the economy suffer from shortages. This is precisely the problem that is likely to result from any socialized healthcare scheme; too much money is pumped into healthcare, and, consequently, too little into some other sector or sectors.
This would not be the case only if the government somehow had more information than the free market: if it knew more about the optimal distribution of resources. I see no reason to do anything but doubt such an assumption.
I must be living in a very different country than you, if all of your compatriots are perenially ill. Most people I know are quite healthy, and would need to call upon insurance only rarely.
Perhaps, then, there should be a high deductible--the insurance company would pay for prescription drugs only if the costs are particularly high.
One's money is being taken away; hence, the right to property is being violated. When the money is used for something like national defense, I think the violation is justified--but here, I consider it unjustified.
But suppose that the product was "essential": water, for example. Would it be acceptable for a store to force someone to buy water, even if he did not desire it? (The fact that water is cheap is irrelevant to the analysis--the essential point is that A is forcing B else to buy something that A, and perhaps society in general, considers "essential," but that B does not wish to buy.)
This situation arises precisely because of the problem I outlined earlier: the failure to emphasize insurance as something that is supposed to cover exceptional and unforseen expenses. High deductible insurance, if only the tax structure did not discourage it, would be significantly cheaper.