Great point, Kiss!  I don't know which of the two was concepted first, or if they were both concepted together, but the sword thing and the prince thing do seem tightly bound.  If you're going to have swords, then that makes the students samurai or princes or something, and if you're going to have dueling princes, then they need to fight with swords or maybe lances.  (Finally, a use for the horses in the opening animation!)  Looking back over the thread, I find to my surprise that I said something similar three years ago:

I wrote:

. . . you can do away with the duels, but they leave a huge narrative vacuum.  You would have to find another way to get Utena and Anthy to meet, to illustrate Utena's protectiveness, to put their relationship in jeopardy.  Now, of course that is possible to do!  You don't even need formalized competition; Maria-sama ga Miteru and Oniisama e, to name two, manage to deal with related themes without a single secret contest behind the school.  But it would be a different show, and you'd have to revise other parts of it accordingly.  (For example, a prince who doesn't fight is a rather different kind of prince than the one SKU envisions, so you'd have to overhaul the archetypes in a way that was thematically appropriate with the new narrative.)

And you also catch that there are even more ideas tied to the prince archetype, like rescuing and being rescued, that are wrapped up with it, to the point where it would be pretty hard to get rid of swords or princes and still have similar themes to SKU's.  As a kind of counterexample, though, we might think about the movie!  The movie has swords, but it doesn't really have princes, or at least not the same way the show does.  The princes are Akio and Touga, and they are dead; neither of them ever holds a sword.  Utena is not trying to become a prince.  As far as I can tell, she dresses boyishly only because she is fashion-forward.  So the movie successfully decouples the "sword thing" from the "prince thing."  The themes don't escape undamaged, but I think the movie still feels like SKU (though YMMV).

KissFromARose wrote:

What other kind of prince could there be without swords? (im genuinely asking here. I cant think of one... except with a guitar emot-tongue, and that version of Utena in which they are all rock band heroes fighting one another sounds like a great concept haha!)

I feel like there is some kind of joke to be made here about Prince, KISS, and Seal (who performed "Kiss From A Rose"), but I've driven for ten hours today and I can't be bothered to fill in the punchline.