The League, as you probably know, is a group of "superhero screenwriters" who encourage, aide, abet, teach, and critique each other in their work (and sometimes lives...). However, to say that we're exclusively screenwriters can be misleading. For the purposes of why we've banded together, having the common goal of writing for the screen is as useful for breaking into the industry as it is for bonding us together. However, we also know that some ideas simply cannot be forced into a medium into which they do not fit.
Imagine one of your favorite movies. I'll use "Glory" for mine. It's a great Civil War movie, with great character and great, but also important, battle sequences. If the author of that story was a playwright and a playwright only, "Glory" would have been about the debate to have an all black regiment. It would have been about politicians discussing the battle. And, if audiences were lucky, it might have culminated in the "giant battle" onstage, or, in other words, about twenty actors with rubber guns running around and jumping into the air when a "cannon ball exploded at their feet." It wouldn't have been the same story.
And it works the other way around. Some plays are great, but would make insufferable films, because there are certain elements that define the mediums. Very few artists can successfully ignore those and make a movie that's really a play but still captivates the movie-going audience. And vice versa.
All that said, as writers, we must recognize when we have an idea that transcends our normal medium. In fact, it can be helpful to try one's hand at writing all sorts of things. I know that for me, personally, I have ideas that seem destined to be only screenplays, or plays, or graphic novels, or comic book series, or novels. And though I'm in a league of "screenwriters," if you imagine the eight ideas I have in my head right now as lights in the dark, the one that is burning the brightest is meant to be a play. I acknowledge that. For my own sake, I had better start writing it now, or soon the light will syphon energy from all the others, until it is the only light still burning in my head.