Keep Burning Those Sacred Cows
Gaming & BS ran an episode where they answers listener questions. One was from a DM who had a player wanting to run a magic user in a no-magic world.
Response to a no magic world: I would think that a GM who has a no magic rule would have a good reason. I would also expect this would come up during session 0. The GM would have explained his world and his reasoning, and the players would have bought in or not at that time.
The monkey wrench: the GM obviously made an exception to the rule at some point. Why? How did it go? Did it ruin the game for the DM (who is also a player, right?), for the magic using character, or for the rest of the group...in any way, including spotlight issues? Did he tell them afterwards that there would be no more exceptions? Yes? Then stick to your guns.
No, he didn't tell them after the last magic user that he wouldn't allow it again? Well then, he left himself wide open for another player to run a magic user!
Now, could it be cool to allow this new magic user PC? Could the GM really control the rate of growth/experience of the character, the rate of spells found/researched, the slow effect this new magic user has on the game world? Yeah, he could! It could be an amazing world building experience for him, his player, and the group. If it happens slowly and organically, it shouldn't get out of hand until many, many years down the road...at which point the PC could very well be dead anyway.
As people listening to the question, we really have to know the GMs reasoning for not having magic users, but it sounds like he could really be missing out if he sticks to his guns.