On the contrary IT handles it rather well IMO. Bill only has one time where he’s notably fluent, and that’s when he’s giving the speech about going into the house to confront the monster. A character makes a comment/joke about how he didn’t stutter, but then the next scene he’s stuttering again. I don’t recall a scene like what you describe in either film and I was literally taking notes on them as I watched them. That said it’s a common enough trope that you’ve likely seen it elsewhere.