Play Blitzball at any time, except when the story is sad

Playing through FFX again, possibly for the 3rd or 4th time in my life, so that I might re-investigate this game narrative's infatuation with death cycles. After you beat the initial Blitzball level in the game, all the save points allow you to return to the waterdome to play Blitzball again at any time. So basically, this means that when one tires of fighting monsters or grows weary of trying to figure out why everyone is growing weary of Tidus, then you can simply say f*ck it and jet away to play Blitzball, provided there is a save point around. This is a bizarre concession which the video game world makes normal because, well, it's a video game.

This suddenly becomes impossible (temporarily) when the game comes to a very poignant set of scenes at about the 35%~40% mark (Summoners' Sanctum scene), when I guess, because of the critical narrative juncture, the player is unable to play Blitzball at save points. I kind of get it--seeing a potentially-heart-breaking scene then suddenly running away to play Blitzball is disfunctional in that immersion-breaking way (and hilarious to me because of my love of the non-sequitur), but the fact that the option is now conspicuously grayed-out is strangely telling of how the game itself wants you to not be able to be distracted from the critical drama point which you have now been served.

I mean, it's not like I was ACTUALLY going to just ignore what just happened and play Blitzball, especially since I suck at that mini-game, but this observation seems to be sticking out in my mind.