In general, we believe that greedy-discriminative solutions are promising for tasks like MT, where there is not a single correct solution: normally there are many correct ways to translate the same sentence, and for each correct translation there are many different derivation-trees generating that translation, and each correct derivation tree can be built greedily following different inference orders.
the set of correct decoding paths is a reasonable portion of UMT's search space, giving a well-designed greedy algorithm a chance to find a good translation even without beam search.