That is interesting. I am writing a musical, so actually the inner monologue aspect of novels can be incorporated through songs, and that is a major part of the art form, and what separates if from plays and movies.
I haven’t studied plays much, but for musical theater at least, I think the biggest difference from novels is that in musicals your characters need to be active. In a novel you can have characters that largely have things happen to them. Certainly they may be quite active, but often you can get away with stories where the main character is dealing with more internal struggles, and has things happen to them more passively. However in a musical this does not work. The main characters need to want something and need to take action to get it. Interestingly enough, I think this is why a lot of the iconic main characters in musicals are actually not very good people. It’s easier to make a character active when they are willing to do anything to get what they want.
Also, if the idea of “show don’t tell” is true for novels it’s like 100 times more true for musicals because it is such a visual, in-the-moment form of storytelling.