I don't think it is so much 'greatness' that makes a film impossible to effectively re-make. Films whose strengths are conventional - great pacing, great but not necessarily iconic performances, great stories etc. - can be effectively re-made (though it may work better as to re-imagine it in some major way, i.e. Yojimbo --> A Fistful of Dollars). The films that can never work as re-makes are those that are the product of true auteurs working in radically iconic styles or dealing with intensely personalized thematic material (say Wong Kar-Wai or early Bergman) or films driven by larger than life performances (like Jack Nicholson at his peak).
Damn, you've just dashed my hopes for a CUCKOO'S NEST remake starring Johnny Knoxville!