I don't think I would have liked it as a minigame but rather as a scripted event like a few people have mentioned.

Though it could have been done like a random encounter system when moving through place to place by airship. It could have been presented like the random encounters in FFT. Then the battles themselves could be the airship itself fighting random imperial patrols and various monsters. The could have made it cinematic by using the ATB system.


Also blitzball is a horribly boring minigame. The only minigame probably worse than blitzball is IX's god awful Tetra Master card game. They are both just terrible and require next to no real skill... and yes I am implying that VII's hoops minigame was more challenging and fun than either of these games.