A book full of years of texts would be an interesting artifact, but how often would you pick it up? How interesting could it really be? Would you even want anyone else to see it?
Now suppose each exchange comes with a haiku summary, a fresh high-level look at the conversation that condenses its vague essence into a little linguistic locket, portable and easily recalled. The interplay between the mundane raw material and the poetic take would render it much more interesting, and tend to reward repeated examination.
A human poet would undoubtedly do a better job at this than an LLM, if any human poet could be persuaded to start and complete such a project. But having an LLM do it would be a very low-cost, low-effort way to at least try for interesting results.