The thing is, people don't speak they way they are taught to write, in complete sentences. Instead, they speak _in actual conversation_ in a series of fragments, which often don't end properly (we trail off, let the other complete our thought, interject, etc), and would be ungrammatical if sequenced together. Remember, language evolved to communicate with others in conversation, not to deliver speeches and text monologues.
Consider this text: "Well the whole point of it was... I mean, when I was in school, we often-- sometimes we would go hunting after school, and I mean, you know -- look, nothing like this ever-- we could never have imagined it."
That's 5 or 6 sentence fragments, one after another. If you processed it in a naively serial way, you just end up with one big ungrammatical sentence. I'm only able to clarify it with punctuation (mdashes and commas) because I could parse it correctly.
A parallel system would benefit not from parsing such a string, but creating a set of candidate interpretations, (all the words together, this is a series of three phrases, this is a series of five phrases, etc) and determining the most meaningful match.