Actually it was the other way around: Greene's original novel contained the 'happy' ending, and it was the US publishers who removed it. Kubrick's movie was faithful to the US version of the novel, and in fact when made aware of the original British publication he was rather dismissive of the ending. Burgess makes it clear, however, that he regards the original 'happy' ending as in fact somewhat more depressing, as Alex reaches awareness that his own offspring (and their offspring, ad nauseam) will probably make the same mistakes as he has, and that he will be powerless to stop them, perpetuating the violence for far longer than Alex himself would be able to continue it.