I disagree, they could have thrown in some dialogue choices, and made the action sequences playable. It would have maybe made the montage twice as long, which is still a very short amount of time.Personally, I think it is a sensible story decision. Playing that at the length it would need to add emotional weight would create a huge content bloat BEFORE the introduction of the primary narrative.
By the time the main game even arrived players would be exhausted and the introduction of some of the important gameplay mechanics would have to be delayed to, er, go dancing. It would destroy narrative tension.
You don't serve narrative dessert before the main course, and the writers were very astute in introducing as much camaraderie as they knew how in as few lines of dialogue as possible.
It's telling that they knew exactly what they were doing that so many people wanted to spend more time with Jackie: they created that emotional investment with the writing that is already there.