Academics pretend to believe that their writings are meant to transfer information intact from one mind to another. This is particularly ironic since they are so adept at preventing any such transfer, using ingenious obfuscatory language. But the model itself is deeply flawed. Words are intrinsically ambiguous, largely by design. When we read or hear another person's words, what we extract is mostly our own invention -- just as most of our memories are reinvented every time we recall them, until eventually we remember exactly and only what we choose.
A better model of communication is that words act as temporary couplings between separate individuals' internal universes. As for most couplings, the strength and specificity of the entanglement is largely due to the prior intent of the participants. Thus a particular horoscope or I Ching excerpt conveys incredibly apropos information if we expect it to. (This is obviously related to the placebo and nocebo effects.) A set of words chosen randomly by a computer from a list can be made to seem deeply meaningful if they are chosen with a bias toward "deep" connotations -- which in turn can be easily identified by simply searching for their frequencies of occurrence in "deep" literature. We fill in the blanks and find meaning in the result. That's what humans are really good at.
So if we think of "communication" as a temporary entanglement of separate realities, it's not hard to see why poetry seems so much deeper than prose: (a) it's expected to be, by both the poet and the reader [placebo effect]; (b) pointless details designed to reduce ambiguity [Ha!] are omitted.
It would be fun to do some "big data" analysis on selected literature to demonstrate this model's validity more explicitly. (Wait...)