As a certified teacher, I can tell you that yes, you can learn how to become "the best GM for every possible demographic" if you actually set your mind to it.
As a teacher I have dealt with kinaesthetic students, I have dealt with squares, I have dealt with problem children and teacher pets, I have dealt with elementary school kids and senior citizens, I have dealt with students with learning disabilities and students who think they know more than I do (and some that occasionally do, even). I'm trained to deal with all types because I'm literally paid to deal with them all.
Does that mean I enjoy dealing with all and every type? Heavens no.
THAT is the question you must ask yourself when evaluating a GM's "quality."
I dealt with more than my share old-schoolers and storygamers and reactive gamers and fishmalks and lone wolves and psychopaths. Do I enjoy dealing with them? Hell no! Would I be prepared to deal with them in my table if I had to? Perhaps... but why on earth would I want to?
GMing is my hobby, not a job. I run the kind of campaigns I want, using the systems of my preference (unless I'm trying a new one, case in which it can go either way), for the people I want to play with. As a result of this, while I may know other ways, I'm more likely to perfect the techniques for what I like to play the most. Furthermore, ever since I learned the most valuable lesson in the hobby (no gaming is better than bad gaming), it's been about a decade since I haven't had to deal with anyone I don't want to. I have way more experience in running games for proactive players than reactive ones. I have lots more games under my belt ran on shared narrative systems than trad/OSR/storygaming ones. I haven't had to deal with players I need to drag kicking and screaming through the flow of events in over a decade, so chances are my skills at dealing with "trouble children" at a gaming table are rusty by now (and then, I screen potential applicants to make sure they'll be a good fit for my table and game in question precisely so it never gets to that point).
So, the question is... sure, as a GM I'm pretty long in the tooth but... am I a "great GM"?
The Answer: I don't need to be. I just need to know what I like, and make sure what I do at the table gets me what I want. As obvious as it sounds, however, it's a harder lesson to learn than you'd think. I know GMs with more flight hours than me who have yet to learn. No amount of time will build Intrapersonal Skill on those unwilling or unable to do self-reflection.
“If you know the enemy and know yourself, you need not fear the result of a hundred battles. If you know yourself but not the enemy, for every victory gained you will also suffer a defeat. If you know neither the enemy nor yourself, you will succumb in every battle.”
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