I was listening to a podcast and the hosts, who are magazine editors, mentioned a headline they had a disagreement over. The article was about poets laureates being removed from their post and the headline was "unacknowledged legislators impeached." When one of the hosts mentioned the headline, someone went ah, in a "that was clever" way, but I'm apparently not, because I don't get it. Where's the cleverness?

"Poets are the unacknowledged legislators of the world." is a quote from Percy Shelley (a poet, an apparently politically active one), so "unacknowledged legislator" is a poetry reference to poets, and impeachment is part of the removal from office, which is what you say the article was about.

Ah, I see, thank you!