A cricketing analogy of what you have describe would be that only all-rounders should be considered for the greatest cricketers of all times since they are good in both batting and bowling unlike specialist batsmen or bowlers who can only be great in one category of the game. A fair argument for argument sake but we can all agree that some of the best cricketers (Bradman, Tendulkar, Warne) in the world were not all-rounders.
As for the crown for GOAT going to the director of the greatest films. I think the directors of all the movies that you have listed other than Shawshank Redemption should be in the running for GOAT unless you have less regard for Orson Wells.
Its hard to look at Orson Wells career and not get awe-struck on how much he achieved at such a young age and how single handedly he transformed theatre (at age 22 he was on Broadway producing, directing and starring in an adaptation of Julius Caesar that broke all performance records for the play and gave him the cover of Time magazine), radio (The legendary "War of the Worlds" broadcast) and of course movies.
He was only 25 when he directed, produced, co-wrote the screenplay and starred in perhaps the greatest movie of all times. It's considered highly influential and its cinematography, lighting, and flashback structure have impacted generations of movies and film makers. Nolan is being talked about in this thread, the plot structure of Memento has its root in Citizen Kane. I can go on and on but you get the point.
Leonardo da Vinci could have only made Mona Lisa and still would have been in the consideration for the greatest painters of all times. Its hard to replicate genius even for geniuses.