Squee's answer to this question destroys the idea of anarchy as a better world or a world of more good. An anarchist might turn to a utilitarian justification to win an argument or convert, but they would surely rely on a logical fallacy somewhere or other.
By the way, you left out the part that hold one of the great problems with utilitarianism: the more happiness for whom? The greatest number. Screed on herd mentality and mass society aside, expecting people to perform mathematical estimations at the point of their decision-making reaches an absurdist peak. And beside, anarchists reasonably respond to such quantification with distrust.
" till you realize that clauses like "for the greatest number of people" is, implicitly, a justification for letting some people fall through the cracks."
i'd raise similar issues regarding "highest quality" and "in the long run".