In Aristotle's Politics monarchy is justifiable if the king has practical wisdom and virtue far superior to his subjects (see, for example, 1284b25-34; 1287a12-16). In other words, the desirability of monarchy depends on the kind of people to be ruled.
The argument, roughly, is this. Humans are political animals and although they share a nature they nevertheless are not automatically equal. We know that Aristotle believed that men are different from women, adults from children, and free people from slaves. This, for Aristotle, constitutes a certain 'chain of command' where children need the supervision of adults, slaves of the master and so forth (1260a f.). But male adults are not equally wise or virtuous either. If a community produces someone exceptionally virtuous, it is natural for this community to accept this person as their king:
In the case of the best constitution, however, there is a considerable
problem, not about superiority in other goods, such as power or wealth
or having many friends, but when there happens to be someone who is
superior in virtue. For surely people would not say that such a person
should be expelled or banished, but neither would they say that they
should rule over him. For that would be like claiming that they
deserved to rule over Zeus, dividing the offices. The remaining
possibility - and it seems to be the natural one - is for everyone to obey
such a person gladly, so that those like him will be permanent kings
in their city-states. (1284b25-34)
Further, it seems that a monarchy is particularly useful for controlling small (and unremarkable) populations. Aristotle muses after admitting that aristocracy is preferable to monarchy "provided that it is possible to find a number of people who are similar" : "Perhaps this too is the reason people were formerly under kingships - because it was rare to find men who were very outstanding in virtue, particularly as the city-states they lived in at that time were small" (1286b7-9). He further notes that as the population grows the favored regime tends to be democracy. That is so, again, because it becomes more and more difficult to find just one really exceptional individual. There will likely be several and in such case monarchy cannot be justified on the same grounds anymore.
To sum up, if having eyes were a virtue for Aristotle (which it is not) his argument pro monarchy would be akin to the old saw: in the land of the blind, the one-eyed man is king.