id suggest that there is no inherent need for mathematical models at all, unless there was a specific desire in the first place to produce said models for some reason. while certainly one would hope that formal models and analysis is performed in the pursuit of some noble/practical end, sometimes it's just fun to research things for the sake of it, because there's always the possibility that in researching one concept, you get exposed to an expanding universe of other concepts that depend on that original one which you never would have considered without the context of the research being performed.

that being said, i think having a formalized way of speaking about the limits of social discourse could be highly beneficial in several different contexts, such as providing effective group therapy, the representation of social interaction in film/literature/etc, and beyond that it can also be used to reason better about the nature of that squishy device that evolved to the point of being able to even comprehend the idea of "conversations" in general, no less the concept of having multiple of them simultaneously