"An art of opening the heart": this is a nice way of capturing the extra-intellectual aspects of memorizing poetry. To memorize something effectively, you have to expend some interpretive effort on it, and with this effort you wind up in something like a conversation with the text. Grasping at least the literal meaning—not necessarily as easy as you might think, I've learned in my teaching—is the most efficient way of mastering a poem, so you can't help but learn something more than just the words in the process. And the richer the text, the more there is to absorb. It's sad that such a truly mind-expanding practice has been saddled with a reputation as just the opposite.
My experience with memorizing in school was a bit strange. I never resented having to do it, when it was actually required (which I suspect was not enough). I actually enjoyed having some bit of verse that I could recall to mind, any time I wanted, unless it was a bit of verse I totally hated (like this Godawful thing, which I'm sure will send Nefarious Neddie into convulsions as soon as he clicks the link, because he sat in front of me in that class and he had to do it too).
And as I noted a short while back, I'm trying to do some memorizing of my own: not poems, per se, but songs, which is really part of the same thing. You have to learn a tune, and you have to learn the words, and you have to learn how the words fit into the tune, and to make it all work you have to figure out just what the song's about in the first place. It doesn't do any good to learn the words and tune of, say, "I'm Glad I'm Not Young Anymore" from Gigi if you don't realize just what kind of mischievous dirty old man Honore really is, and what he's getting at when he sings it. And it's really fun to just be able to drop little bits of verse and song lyric into idle conversation, once in a while. If you want to sound like you're an erudite individual, well, here's a great way to do it. And the best part is that it will actually make you erudite.
The part that I seriously hated about memorizing in school wasn't the actual memorizing, then. No, it was the fact that teachers felt the insatiable need to couple memorizing with reciting, which I despised as much as is possible to despise anything. Bad enough that you have to stand up in front of your classmates and fumble through a poem, but even worse if every kid in the class is doing the same damned poem, so you're spending forty-five minutes in a hard-wooden chair listening to the same poem over and over and over and over and over again, while Mrs. Hairbun dutifully takes down notes on each student's delivery. It always seemed to me that simply giving everyone a piece of paper and requiring them to actually write down the poem would have accomplished the same goal, without being simultaneously boring and nerve-wracking; moreso if the actual goal was to learn a poem as opposed to being expected to put on a bit of performance art (woeful grades to the student who delivered every syllable perfectly, but with a monotone that would make Mr. Spock proud).
Anyway, maybe I will start memorizing poems. It seems a good way to simply exercise the brain a bit, and you never know when the ability to start spouting some Tennyson at length might come in useful.
(Lynn Sislo also comments on this. I actually read her post first, but I would have read OGIC's sooner or later anyway, since I read About Last Night daily. Did I already mention that?)