That seems really, really flawed, methodologically. As I said linguistics is about as far as you get from my field, but as a layman that still seems wrong on an ‘the earth is flat’ tier. Why would you analyze something that we see used everyday as a ‘defective’ sentence? That’s like a cultural anthropologist saying that Native American raindancing is a ‘defective garden sprinkler’. Do you have any insight into why this idea is widespread? Am I making ignorant assumptions?
Well, anthropologists have a history of analyzing the rituals of "primitive' communities as "defective" versions of things we do. It's a question of how you model your object of inquiry. For linguistics it was, for a long time, etymology, and, then, more recently, grammar. If you're thinking about words, and parts of speech and grammatical rules, then you're thinking about sentences. So, if someone says "open the door," it seems natural to view that as a shortened version of "you are to open the door." In terms of sheer meaning, it seems to be the same thing. So, you say that "open the door" has an "implicit subject" ("you") and you can treat it as any other sentence.