Actually, some of the greatest composers of film music were the well known 'classical' composers of the 20th century. None of those you mention can hold a candle to Prokofiev in his music for Alexander Nevsky (candidate for the greatest film score ever written?) and other Eisenstein films. Other noted composers who produced great film scores were Vaughan Williams (Scott of the Antarctic), William Walton (Henry V etc), Honneger (Les Miserables) and Korngold (Elizabeth and Essex, The Sea Hawk etc). The you should not forget the Hollywood composers of the 'golden age', the likes of Max Steiner and Andre Deutsche. Another 'great' that you ignore is Bernard Herrmann - ever seen Hitchcock's 'Psycho' or Jason and the Argonauts??
Later - I see del_icio has posted whilst I typed the foregoing. I dispute his contention that this music is not 'classical' (in the widest sense). Film music can be, IMO, and the best is equivalent of the 19th century habit of having leading composers write incidental music for the theeatre, the best known example being, I guess, Mendellsohn's music for Shakespeare's 'A Midsummer Night's Dream' But I recollect that I and d_i have argued this point before on here and neither of us will concede to the other!