Private roads already exist. There are neighborhood roads in various places that are maintained not by municipal governments, but by homeowner’s associations. There are toll freeways in our larger cities that you have to pay to drive. This is often done using a transponder that detects when you get on and automatically bills you for it. The old fashioned way, of course, is gates and toll-booths (kind of like at the Golden Gate Bridge), but new technology is making it so that kind of delay is unnecessary.
As to Democracy’s ability to model an absolute free-market system, it is quite unable to do so. The model makes the assumption that, if the government is not providing certain services, those services are simply not provided, which certainly is not true in real life. Everything that needs doing will be done, since anything that needs doing can turn a profit for the one doing it…
Education existed long before public education, both in the forms of well-paid tutors for the rich, and apprentiships, church schools, and such for the poor. There is a large and very effective system of private education in the US today, not to mention home-schooling, which is in many respects superior to public schooling.
As I mentioned earlier, there is such a thing as privately maintained roads, as well as communally maintained roads (not by taxation, but by voluntary contribution). In addition, I suspect that, were the US government to stop subsidizing road building, we’d see a lot more privately built “mass transit,” since it’s probably easier to charge admission to a train than a road.
In a society with relative political and economic equality, basic military protection can be provided via voluntary, unpaid militia service–and such a model is actually safer than the model which concentrates military potential into the hands of few in peacetime.
A society in which access to land has yet to be locked out finds immigration to be a blessing, and has no need for anti-immigration defenses.
One of these days, I might create a mod which, if proper conditions of economic equality and absence of government funding are reached, it produces an event called “The market takes over!” which results in services being provided without government spending.