Philosophers use evidence all the time in support of their arguments, especially when they are making empirical claims (as you are: you are claiming that the costs of government outweigh the benefits when it comes to the provision of public goods). If you choose to not use evidence, then it is important to be far more careful and charitable than you have been. E.g., in your "simple argument" you only consider examples at the extreme (million -x benefit or 1% ROI). These are straw men -- you don't in fact deal with any kind of realistic example.
For your reasoning to have been good and fair, you would have had to consider the scenario that puts your position in the worst possible light and then show that it still holds. Imagine a dam that costs $100 but provides $10,000 of benefit to 20 users. Imagine, further, that all 20 users are competing with each other for status and customers, they are all roughly equally wealthy, and that paying for the dam will be a significant expense for most of them. Even though the dam could be built by any five of the users, any user who doesn't pay will gain a comparative advantage over the others. The libertarian might propose that they collectively participate in a contract. But why should anyone agree to participate in this contract, if they know that the dam will be built irrespective of their participation, and if they will get an advantage over others by not participating? No doubt the hold-outs will claim that they can't afford to pay for it, or that they don't want it -- but this is just a negotiating strategy.
Sure, setting up a government to deal with the provision of a single collective good is extremely inefficient. The issue is that there are many thousands of such public goods (and services). The empirical argument, here, is that on balance the inefficiency is worth it.
It does not appear, from your essay, that you have carefully and sympathetically examined the relevant counter-positions. If you haven't already looked at it carefully, I would recommend http://plato.stanford.edu/entries/free-rider/
It is interesting that free market fundamentalists seem to have trouble deciding whether their argument is an empirical or a philosophical/moral/ideological one. They will claim that libertarianism is the answer because government-based collective action is always less efficient (an empirical claim). When evidence is provided that this need not always be true, they switch to an argument of "freedom" and natural rights. When this argument is shown wanting, they then revert to their efficiency-related arguments. This flip-flop frequently works to fool many, it seems.
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