I absolutetly adore FC's poem! It's so funny with all those additions by the squabbling PB and Ilbereth!
Perhaps this is no "literary poetry", but I actually think it is much more deserving of the title "poem" than modern so-called poems which don't rhyme, have no rythm at all and are in reality just prose, written in short lines!!
(a propos funny poems, I am a bit reminded of Christian Morgenstern...don't know if you know him, Esty)