Poetry has nuisance value.

“Nuisance value” is the value of a frivolous insurance claim or lawsuit: the amount the entity on the receiving end will pay you, even though your claim is meritless, just to make you go away. It’s a measure of the overheads of whatever system is used to resolve such claims - the cost, to the winner, of winning without having to fight over anything of substance.

More generally, then, nuisance value is a measure of the noise in the system. In the case of language, poetry presents what may be frivolous demands on the hearer’s time and cognitive powers. Its claims are not transparently resolvable. There may after all be something in it. You will have to pay a certain amount of attention in order to find out whether there is or not. (Even poetry that is limpidly accessible, forthright and direct may actually be disguising an underlying vacuity). A poem is a bid for the share of attention needed to look into the matter. Its value is precisely what would pay the poet to shut up, go away and stop bothering you instead.