In theory, if we had a very good LM trained on huge amounts of data, the kind of errors that can be corrected by a monolingual posteditor (GALE), which are generation, fluency errors, should be already taken care of by such LM, right?

The problem is that even LMs trained on really large datasets face sparseness problems for high-order models. From a practical point of vew, since the number of parameters of an n-gram model is O(|W|^n), finding the resources to compute and store all these parameters becomes a hopeless task for n > 5. Or even if we did (read Google did), in actual text, the majority of n-grams that one sees are bigrams or at most trigrams, and it’s very rear to see very high n-grams.

Therefore, current LMs, in spite having smoothed and improved MT output, still generate disfluencies.

An aside: I love the term lexical miopia and shortsightedness to describe low n-gram models (Beeferman et al. 1997).