I had to memorize the first few pages in ME in high school. Not sure reading the whole thing that way would be pleasant, unless you are a serious English Lit History buff or poet. But it certainly a more melodious version, so if you do I'd recommend reading it aloud.
I am, dubiously, both (and in the midst of wrapping up a dual Lit MA / Poetry MFA program). Medieval poetry isn't really my area of study, in either purview, but—thanks to a final required seminar—I've been reading Chaucer in the original (along with criticism) pretty much exclusively for the past three months. It's pretty wild how quickly reading facility comes, relative to truly distinct languages: initially, it was taking me about an hour per hundred lines, but now I'm reading five times that closely, and maybe as much as ten times that if I'm skimming. Some colleagues in the class have "cheated" and gone the route of reading a "translation" first, then skimming back through the ME, but in retrospect I'm glad I was obstinate.
I enrolled in an Old English course in undergrad, but dropped that before the three-week withdrawal-deadline;
that reading-practice seemed a lot more unpleasant, and like a
truly distinct language. As medievalists like to point out, the span between Beowulf and Chaucer is the same as Chaucer to present, but the language changed much more dramatically during the former than the latter.
I have a student who now has her PhD in Linguistics and she could read Mid English and used to read and translate her Mid English quotes to me as we worked on her Masters and Doctoral theses. It's beautiful, but strange to hear a dead language.
Had to memorize the first 10 or so lines of the prologue in hs. An odd thing to have to memorize.
It seems it's actually pretty oddly-common, at least judging by my anecdotal sample. My high-school in NW Florida gave us choices (during sophomore-year English) of the passages for mandatory memorization, and the opening of the GP was amongst those; I don't think anybody took that route my year, but I wish I had, since at that point I still had a nice soft adolescent brain for memorizing whatever. Instead, I still have "easy" poems like
We Real Cool,
Fire and Ice, and
The Red Wheelbarrow forever mnemonically lodged in my brain; meanwhile, if I try to memorize a poem or passage now, it's gone in a month without some sort of active maintenance.