Am I missing something?

Yes, because linguistics has always essentially "forbidden" any inquiry into the origin and development of language. It takes fully developed languages as its starting point. So, insofar as they analyze imperatives and ostensives, it is as "defective" or "elliptical" sentences.

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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.

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Gans has a whole series of Chronicles from back in the early 2000swhere we goes through a whole series of hypotheses regarding the origin of language.