The films I know of that have a character who stutters are King's Speech, My Cousin Vinny, Fish Called Wanda, and the stutter is somewhat problematic in each, in that it's a punchline or something to be "overcome" or defeated. I was intrigued by Leo DiCaprio's stutter in Once Upon a Time in Hollywood. It seemed he made a choice to give his character a stutter, but not overtly play to it. I thought that was pretty brilliant and I'm surprised people don't talk about it much.