Why do we never hear actors stutter or stumble over words in movies?

Why do we never hear actors stutter or stumble over words in movies? It would be more realistic for them to add it in the movie. Or.. would that undermine the character being portrayed? I've seen instances of false starts/stuttering on TV and movies, but it's never by a main or "powerful" character. Maybe the MC needs to sound enjoyable, confident and sympathetic? Can't they do that with a stutter?