A single person cannot rule a country directly. They have no time to make every single blacksmith pay his taxes, to judge about every lawsuit between a lord and his serfs.
A king would rely on his feudal retainers, who rely on their feudal retainers, and so on. Such a system could rely on the "common delusion" of legitimacy -- the nobles must believe that being the son of a king makes one fit to be king, because otherwise what qualifies them to be dukes or earls? Or it could rely on the "collective action problem" -- the first one to resist the king would die, even if the king would be deposed in the end if all nobles resist. Or a mixture of both. And of course the king would back a duke against a peasant revolt, because otherwise the whole social order might tumble.
Perhaps mages could form a similar system, with greater mages ruling kingdoms and lesser mages administering counties in their name. But the great mages would soon notice that a decent administrator or war leader makes a better subordinate. And sooner or later the son of a great mage does not become a great mage himself.
So plenty of dynasties in your setting might have started with a mage, but then they became ordinary nobles over a couple of generations.