I think the principle of [Chekhov's Gun](https://en.wikipedia.org/wiki/Chekhov%27s_gun), originally from from playwrighting but applicable to movies, applies here. If you're going to hang a gun on the wall in the first act, it must go off by the third. Essentially, don't introduce any unnecessary, conspicuous details to your storytelling (for several reasons). A character's stutter will be noticeable and potentially distracting. Unless it plays a narrative function or adds significantly to the character, it's not a detail worth including. You don't see characters in wheelchairs unless it's to show frailty, past trauma, or play a role in preventing them from doing something later on. Same with any other quirk or idiosyncracy that would make a character more realistic or representative of any random person in the world.