I would agree that it is not "the government"'s job to provide education, since there is no valid reason to use force / aggression as part of educating people.
You're right, Phil. That's ONE of the mechanisms society uses to accomplish things. That's not the only mechanism, and it's certainly not the appropriate mechanism for many things.
I'll give you a concrete example.
In my state, the Department of Transportation only plows snow from arterial roads, not from neighborhood roads. In order to get snow plowed on a neighborhood street, residents have to organize a civic association that collects dues, and those dues are used to pay for plowing; the state then reimburses the civic association for a portion of its expenses. But because membership in the civic associations is entirely voluntary, we end up with a 30 percent participation rate. My share of the dues, in effect, pays for not only myself but two of my neighbors who aren't willing to pay their fare share.
That is ridiculous. It is a perfect example of a case in which it is simpler and fairer for a couple of bucks to be added to each household's property taxes and have the plowing be publicly funded (although it could still be privately plowed).
Furthermore, the idea that the only role of the government is in situations where force is necessary is pretty darn limited. You might have a case if you're talking about national government, but I imagine that the bulk of the tasks your municipal government takes care of, outside of police work proper, don't require acts of aggression.
In a truly free society, there would be no such thing as "public property". It would all be private, and usage of that road would have to be paid for by those that want to use it. And the owner of said private property would maintain that property such that it would provide value for all those that wish to pay for usage of it.
Did you ever consider that maybe those individuals on those houses don't use those roads? Maybe they walk, bicycle, or are plain hermits? (Odds are they aren't, but I'm sure there are a few). You want to work with absolutes, and then deny that aggression is present. Do you want to argue that taking money from someone in return for something they don't use is not aggression? How about a thief taking money from your wallet on the counter, and then handing you a sack of grain in return? Would you say that's not aggression?
So I think it's fair to say that a public system has drawbacks but being generally less free than a private system is definitely not the case.
Tis called the "Free Rider Problem." Governments are constantly trying to solve it.