David Friedman makes a pretty good argument against this. If you look at the police in big cities where they have many more officers and much larger budgets you actually see less satisfactory service than police in smaller cities. According to what emperical evidence is available on this subject, it would appear to have INVERSE economies of scale, i.e. smaller police forces provide more satisfactory service than larger police forces.
What you say, well, what David Friedman (who is him?) says may very well be true. I didn't say that every state would be perfect, but, firstly, you can't deny there is such a notion as economies of scale or that they actually work. Secondly, there is a law of diminishing returns which further complicates things. And thirdly, big cities require more officers and larger budgets not only because they are bigger (this is beyond discussion for obvious reasons) but primarily due to a wider range of specialized services they demand (i.e. more fine-grained division of labor)...