The two common explanations for vagueness/ambiguity in language come from Zipf and Chomsky, and both seem to inherently assume that vagueness/ambiguity do not serve a positive purpose.
In the case of Chomsky, ambiguity arises out of the constraints of the mind at parsing language. Once again, this assumes speaker-and-listeners want to communicate perfectly.
In the case of Zipf, ambiguity arises from the conflict in energy investment between the speaker and listener. The speaker wishes for a totally ambiguous language where they can use one sound to mean everything, and leave the difficulty of disambiguation for the listener. The listener, on the other hand, wishes for a totally unambiguous language, so the difficulty of picking the right words is on the speaker, and the listener doesn't need to spend energy on disambiguation. Note, that this approach still assumes that the speaker-listener pair still have the goal of conveying a single meaning from one to the other.
Some recent work (pdf) even formalizes Zipf-like ideas to prove that ambiguity is essential to allow communication between parties with different priors. However, their approach relies on speaker-listeners that want to maximize the probability of conveying a single meaning from one to the other.
However, vague and ambiguous language, is often used on purpose by the speaker in order to have the listener select the meaning they most desire, and not necessarily the one intended by the speaker. A common example would be campaign promises from politicians, but the concept is often used for more artistic and pleasant purposes through songs and poems. Some go so far as to say that vagueness and ambiguity is what allows creativity.
Are there any theories (hopefully formal/analytic ones) that look at vagueness and ambiguity from a positive perspective? Or at least ones that don't presuppose that the speaker has a single meaning to convey to the listener or that the speaker-listener want to maximize their agreement on an intended meaning?