Were you the guy who just x'd through all of the dialogue?
The song worked because of Jecht, & it was havily foreshadowed. Remember when Sin was at Macalania Temple? How it was just floating there, not attacking anything? It was because of the Hymn. Or how it wouldn't attack Tidus? That was because Jecht didn't WANT it to. This is also why it isn't using some of its more powerful attacks. The song just gets Jecht emotionally charged, it doesn't magically weaken Sin. But Jecht can only hold it back to a point, & his control is fading throughout the story, as he's fighting a constant battle there.
The party also had its own advantages. For one, an airship. Operation Mi'ihen involved a fucking calvalry charge. Arguably, the ship, besides allowing them to fight more on its terms, allowed them to get close enough to notice Sin had weak points that could be targeted. They also had their own summoner who WASN'T secretly trying to screw them over.
Plus, that WASN'T the party's ultimate plan. They only needed to confront Sin in order to get inside of it. While Operation Mi'ihen came close to "succeeding," it would have still failed because they did not account for Yevon.
Could the party have done the final assault at Mi'ihen? Probably. But they would have likely been slaughtered. Having the rest of the Aeons, the emotional growth, & all of that jazz greatly increased their chances. That's probably why Auron didn't say anything about Yu Yevon. And Seymour probably didn't just because he was a damn loon.
TL;DR: It's not really Videogame Logic if it makes sense.
