The idea of a extended Blitzball game was actually brought directly to Yoshinori Kitase (FFX Director/Producer) and Motomu Toriyama (FFX Event scenario director/writer). Here's the clip where they receive the idea:

http://youtu.be/NrNLr8DSbw0?t=18m7s

As for having it a part of FFXIV:ARR, it's probably going to be too much work for the developers and wouldn't fit lore wise anyway.