Paperwork is a significant part of being a Student Council President, but so is being a bit of a figurehead. Ideally, you want somebody with at least some charisma in that role, and Honoka does have charisma in flying colors. I think that this might be particularly important here given how this school is just now recovering from near-death. Yes, they have saved the school, but they might want to further cement that recovery by fully cashing-in on Honoka/Muse's popularity. After Eri graduates, it will be Honoka that will be welcoming all the new first years. and that would be very fitting for those first years who chose this school largely because of the efforts of Muse.
So while I was pretty surprised at Honoka becoming Student Council President, I do think she's better-suited for it than some other members of Muse are. For example, I'd take her over Kotori, as Honoka is the much more decisive and emotionally strong of the two girls.
Aside from all of the above, I like what Candyshark wrote above.
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