Rothbard wonders exactly how much and what kind of protection ought to be given to whom:
there is a vast range of “defense” services that the government (or any other defense agency) could supply to its customers. To take two polar extremes, the government could supply one unarmed policeman for an entire country, or it could sink most of the national product into providing an armed bodyguard, replete with tank and flame throwers, for every citizen. (“The Myth of Neutral Taxation“)
There is no non-arbitrary way to determine the optimal amount of protection, he claims.
I think there is a simple answer to that worry, though: it is necessary to produce publicly just enough defense for the defense force to overpower any private person or group in society against which there exists a judicial sentence to be enforced.
If a judge has ruled that company C owes person P $1,000, then C should have no chance in an open armed confrontation with the cops. The police force should be powerful enough to crush any resistance. They beat criminals into submission, capture and hold them, and punish them. There is simply no private replacement for this function.
On the other hand, that is all the cops ought to be able to do. For example, they should not be in business of supplying security (including such as may be provided by tanks and flamethrowers) but only reliable enforcement. Thus, if a town has 50 cops, and only 30 is sufficient for that task, the mayor should fire 40% of the personnel and lower the local tax rates.