In our non-magical reality, feudal nobility is postulated to have evolved from warlords - an armed man in charge of a group of armed men. Since they can intimidate less-well armed or trained people, they are effectively in charge. Then, as they must defend their territory against other warlords, they must gain the cooperation of the people they rule (or they might defect), hence the social contract between vassal and lord, and when a stronger warlord comes along that both know that one cannot defeat the other, the lesser warlord becomes a lieutenant to the stronger, hence chains of fealty.
Now, suppose that we have a world where magic exists , and magicians (very similar to the magi in the Ars Magica RPG, who are quite rare due to some semi-random magical factors that only combine fortuitously in a few individuals) must study for many years to gain their powers. An apprenticeship is 15 years long, and is typically begun at ages between 4 and 7. To gain in power noticeably, a magician must study for months, and the greatest typically spend the majority of their lives in study - think of them as being like research scientists in that respect.
However, these magicians, once they become sufficiently powerful, can achieve many things. They can extend their own lives to as much as a couple of hundred years or so. A combat magician could devastate an army without magical support single-handed. They can control the minds of others, build and destroy rapidly, control the elements, create illusions or go unseen, all with only a few limitations, based on the amount of study they have put into each area.
In the Ars Magica RPG, which is based on medieval European history, these magicians are explained as not being interested in temporal rule, and are all members (on pain of death for refusing to join) of a secret group that enforces this secrecy and detachment from mundane society, as well as their magical abilities making most of them just feel wrong to mundanes to a greater or lesser degree.
However, how realistic a scenario is this? We have a small minority of people with great magical power who certainly have the ability to rule effectively, more so than some thug with a sword and delusions of their own self-importance. They can use their magical arts to divine the will of the people or alter it, and can reliably get to the truth of a situation regardless of the lies the mundanes might try to tell unless another magician has interfered.
However, to achieve these capabilities, they must first have studied for as much as half a mundane lifespan - probably on the order of 30 years from age 5 or so - and must continue studying around 90% of the time if they want to continue advancing their skills.
So: Would these magicians want to be in charge, given that the demands of governing would detract from the time they might otherwise spend in study, and that if they spent any significant time governing, their advancement would suffer and leave them open to conquest by a magician who had studied more? What might government look like in this scenario?