Thank you for recognizing the situation I was in! (Nit: "to be or not to be" is probably a bad example of something that depends on iambic for memorability.)
Also, when I tried rewriting that soliloquy for modern ears, it didn't even occur to me to keep the meter; that never registered as a noteworthy aspect of it.
One other thing: keep in mind what it's like to be in high school. For the vast majority of your life, you're told to do things "because I said so". So the idea that there might be an actual good reason for stressing Shakespeare the right way ... didn't stand out as an obvious hypothesis.
I'm curious: does any poetic metre stick out to you as 'nice' or making texts easier to remember? Or is this just some part of the human condition that's completely alien to you? I've heard similar things from some people about music in general ('it's just noise; I don't see why you think it sounds nice'), so it wouldn't really surprise me if that were the case.
Meter does matter to me, and I do enjoy music. Just the every-other-syllable stress with natural stresses in iambic pentameter doesn't resonate.
In the lightning talk, I contrast IP with ska music, which I like, and which is characterized by stressed off-beats (which resonate with me) and mis-stressing the syllables to fit the meter (which also resonates with me).
Edit: Another thing about the high school experience: Shakepeare kind of fit a pattern of "stuff everyone professes to like but whose enjoyment seems to be fake/performative" (along with pop music, sports, and the taste of alcoholic drinks). I joke that if I were gay, I'd include everyone else's apparent heterosexuality in that pattern.