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In fantasy, mages are commonly described to be vastly superior in terms of knowledge & power to the rest of the population. Typically, they live much longer, are able to kill in combat numerous non-mages at once, etc etc, and on top of that are typically the most educated caste of the society. And yet, while sometimes influential, they are the kings' advisors at best, but not kings themselves.
This seems odd to me. Given all of this the mages could easily take over the whole society and establish magocracy. Works of fiction often wave this issue by claiming that mages are too focused on studying to look to gain political power; an explanation that doesn't seem compelling to me.
How can this be really explained?
Perhaps we could look at our society and draw parallels between fantasy magic and science. Could Einstain or Hawking take over the society? No, but not only because they wouldn't want to try - they would be clearly not able to do so. And yet Einstein helped to devise one of the most terrific weapons the world has seen - the nuke.
Maybe, then , the key is to say that those who study theoretical magic and are responsible for advancements in the field (Einstein, Hawking, etc) are not those who apply magic, whether for combat or civil purposes? We would therefore see at least 3 different sorts of mages: Those who, shut within towers & universities, faciliate theoretical advancements; those who craft magic artifacts ("factory workers"); and those who apply magic for practical purposes (battle mages ~= irl soldiers, as well as other civillain, non-warfare occupations). Seems to make sense: A soldier neither crafts his rifle (= wand / other artifacts) nor is able to invent more technically advanced rifles; but works of fantasy usually forget this distinction and make the same people responsible for theoretical advancements, production of artifacts and practical applications.
Yet this still doesn't seem too correct... Eg even irl scientists are able to found start-ups and start applying their science for practical purposes! So there is not such a sharp distinction as I would hope for.
How to have mages that will plausibly not be able to take over the society?