It doesn’t promote anarchy per se; it’s a bit more complex.
In Liberalism, Mises himself wrote:
We call the social apparatus of compulsion and coercion that induces people to abide by the rules of life in society, the state; the rules according to which the state proceeds, law; and the organs charged with the responsibility of administering the apparatus of compulsion, government.
There is, to be sure, a sect that believes that one could quite safely dispense with every form of compulsion and base society entirely on the voluntary observance of the moral code. The anarchists consider state, law, and government as superfluous institutions in a social order that would really serve the good of all, and not just the special interests of a privileged few. Only because the present social order is based on private ownership of the means of production is it necessary to resort to compulsion and coercion in its defense. If private property were abolished, then everyone, without exception, would spontaneously observe the rules demanded by social cooperation.
It has already been pointed out that this doctrine is mistaken in so far as it concerns the character of private ownership of the means of production. But even apart from this, it is altogether untenable. The anarchist, rightly enough, does not deny that every form of human cooperation in a society based on the division of labor demands the observance of some rules of conduct that are not always agreeable to the individual, since they impose on him a sacrifice, only temporary, it is true, but, for all that, at least for the moment, painful. But the anarchist is mistaken in assuming that everyone, without exception, will be willing to observe these rules voluntarily. There are dyspeptics who, though they know very well that indulgence in a certain food will, after a short time, cause them severe, even scarcely bearable pains, are nevertheless unable to forgo the enjoyment of the delectable dish. Now the interrelationships of life in society are not as easy to trace as the physiological effects of a food, nor do the consequences follow so quickly and, above all, so palpably for the evildoer. Can it, then, be assumed, without falling completely into absurdity, that, in spite of all this, every individual in an anarchist society will have greater foresight and will power than a gluttonous dyspeptic? In an anarchist society is the possibility entirely to be excluded that someone may negligently throw away a lighted match and start a fire or, in a fit of anger, jealousy, or revenge, inflict injury on his fellow man? Anarchism misunderstands the real nature of man. It would be practicable only in a world of angels and saints.
Liberalism is not anarchism, nor has it anything whatsoever to do with anarchism. The liberal understands quite clearly that without resort to compulsion, the existence of society would be endangered and that behind the rules of conduct whose observance is necessary to assure peaceful human cooperation must stand the threat of force if the whole edifice of society is not to be continually at the mercy of any one of its members. One must be in a position to compel the person who will not respect the lives, health, personal freedom, or private property of others to acquiesce in the rules of life in society. This is the function that the liberal doctrine assigns to the state: the protection of property, liberty, and peace.
Mr. Rothbard might not agree, but I think this is fairly reasonable.