I think a significant part of why they heavily relied on the "bonds" concept was because it was a fighting game. They had said something to that effect in an interview, about how exploring the tenacity of the Investigation Team's friendships and how Shadows never truly disappear were things they wanted to explore, and how a fighting game was the venue to do so. When constructing a story to fit around the concept of them fighting each other, I guess that was the logical place to go to, story-wise, since it fits around the format of them fighting each other, while also combining the P4 themes they wanted to explore.
This is why I think that, if there was to be a P4A3, going with the Xrd story model could potentially do a lot of good to the game's story, where they're not shackled to the expectations of the genre and are basically given the freedom to do what they want to with the story.