As far as infrastructure you can take a look at this. http://www.youtube.com/watch?v=MseBlo-Sno0
Personally I think that infrastructure is far less of a problem than, for instance, security for children. Remember, that in an anarcho society there would not be NO LAW, law would be created through voluntary contracts. Towns may come together and build their roads socially but funds would not be taken through force. This type of situation would make it very attractive for businesses to help fund the roads to get people to their businesses.
As far as private police you can look here mises.org/journals/jls/14_1/14_1_5.pdf
What to do about child abuse and the like you can see some correspondence between Walter Block and someone with similar questions here http://www.lewrockwell.com/block/block167.html
That all being said, I do partially agree with you. I have questions about the abilities of a stateless society to deal with the threat of a large scale or nuclear war and the like since, for one thing, should the world never have developed the state, things like nuclear weapons would be very unlikely to ever have existed. I also have questions about the ability of a new stateless society to remain just when men are corrupt and large businesses are likely to buy up their own police forces and enforce their will. Large forces beholden to an interest is what created the state. Again these types of large companies may not have been able to grow to the size they had without the protection of the state.
BUT, I cannot completely reconcile the ability of the state to use force to collect taxes to fund these things with the principles of individual rights.
Hope most of that made some sense.