Without the courts (paid for by taxes)
You've never been involved in a civil case have you? The participants in the case pay court (or arbitration) costs, its not some service you get for free paid for with tax dollars. This ignores other costs or accessibility issues.
As far as national defense is concerned, this will likely not be paid for on a voluntarily basis.
Because people cant defend themselves? The worlds most powerful military couldnt conquer a nation of goat herders, in a area smaller than Texas, with a population only 8-9% of the US's and a fraction of the number of arms in private hands.
b-b-but muh roads!
Private companies build them, not the government.
Criminal cases are ultimately paid for by tax revenue. You also have "court costs" in civil cases but this will not necessarily pay for all of the costs associated with the case.
If you had someone stalking you and needed to take out a restraining order I doubt you would want to have to wait two weeks to get paid before you can pay the filing fee.
I am not sure what war you are referring to in the most powerful military not being able to conquer a nation of goat herders. I do know that war is much more complicated then that, especially if you are fighting far from where your country is.
Who do you think pays for the roads? For the most part motorists do not pay when they travel on an interstate or a "street" Granted there are some toll roads but they are a minority. The government contracts private companies to pay build roads, and pays them for their services. Hence the government pays for the roads.