as far as public infrastructure, i think private companies will create roads.. but then you'd have toll roads everywhere. and since men are not created equal, one guy might climb to the top of the ladder and own all the roads. what happens then, when he charges you exorbitant fees?
That's a terrible business model
Nobody would drive if you charged to drive on them, and then how would businesses get consumers? The point of roads is to lead to business, not to charge for the privilege.