Where do you derive the word "stats" in "Role Playing Game", I can see the words "playing" like play, and "game" like in a game, and then I see "role" like a role you take upon yourself, a role that is defined by the characteristics of the character and its actions, yes I know stats play a minor role in the RPG aspect of a game seeing how for example it would be bad if "Brutus Biggus" the giant managed to sneak better than a master thief because of player skill, so stats do help define a character. But finishing moves is something I think you can ignore, and in fact I think that if you were playing our friend Brutus Biggus, then you would also be able to ignore your mastery at sneaking for the sake of in game realism.
So back to the question of if finishing moves can work in an RPG ? Well yes. If poorly implemented they can come out wrong of course but if done right, for example if you earn your finishing moves through the mastery of your skills then yes finishing moves can turn out to be brilliant. But even if "Mini Maggie" the mage can do a backflip and a 180° spin in the air throwing needles into the neck of her enemy finishing off with a slash over the throat before even landing as a finishing move, then while I will find that to be unrealistic and bad, but I will be able to ignore it. Then I can just enjoy using the finishing move on "Slicing Sam" the assassin as it was a finishing move intended for him to use.
I call for self restraint for now unless it becomes an aspect of the game you cannot ignore, like if you must do a super mega finishing attack to do an essential quest or something of that sort.
Edit: If finishing moves are not optional to use I am going to cry tears of blood