Runing multiple systems will give you different perspectives. You will learn how different mechanics solve same problems. It can be valuable if, and that's big if, you pick system that's good at something specific.
To ilustrate point. You only ever ran 5e d&d. You like it, but tactical combat isn't really best in 5e. If you pick up 4e or PF2, you will get valuable experience on running tactical combat. If you pick up Houses of the bloodied, you will learn nothing about tactical combat cause that game doesn't have it.
So, when time is limited, branching out needs to be thoughtful. You need to find pain points in system you run for type of games you wanna run, then find system that does those things good. It might give you ideas you can incorporate in your main system or how to tweak it to work better.
I would argue that you can learn and run 10 different systems, have solid system mastery over all of them, and still be bad dm ( i consider bad dm someone who: railroads players by forcing them into a predetermined story, acts adversarial by trying to "beat" the party, applies rules inconsistently or unfairly, ignores player agency and character backstories, hogs the spotlight or plays favorites, neglects consent or player comfort, refuses to improvise or adapt, paces the game poorly or shows little preparation, and uses their authority in toxic or belittling ways that undermine player enjoyment ).
I agree, but if this is a 2000-lb argument, 1999 pounds of it are being carried by a single word:
can. You
can still be a bad GM even with this experience, and you
can become a great GM even without this experience.
But that is like saying that someone
can be a terrible writer despite having read and carefully studied a thousand different authors' works, while someone else
can be a profoundly sublime author despite having never read even a single line of anyone else's prose. Yes, there is a vanishingly small probability that a person could just be naturally amazing at writing books without any training, experience, or effortful understanding of the craft. Yes, there is a small (though not nearly as small as the previous) probability that someone who has carefully studied and genuinely understood many works of literature could still be just objectively and unequivocally terrible at writing prose.
For the
overwhelming majority, however, reading and understanding the work of lots of authors is critical to being a good writer yourself, and very few of the great authors in human history would have been nearly so good if they had actively refused to read any books they didn't personally write. It is, simply, a fact that in any creative medium--and GMing is a creative medium!--you should engage both deeply (digging far on one specific area)
and broadly (digging into many different areas, albeit rarely quite so deep).
Isaac Asimov was a better science-fiction writer because he was also a nonfiction (and particularly textbook) author. And, I'd argue, he was also a better textbook author because he understood how to write good, interesting, compelling science fiction, especially the type he personally specialized in, ideas-focused fiction rather than character- or plot-focused fiction.