Blitzball plays a big part in Spira. Yoshinori Kitase used the sport as inspiration but because it’s a “world sport”.

In the Blitzball world, people revere Jecht. I guess you can say he’s similar to a Pelé in that respect. Even Tidus remarks how the announcer gushes over his father.
In Tidus’ day, blitzball looked like a state-of-the-art sport. Check it out: flashy cameras, advertisements, professional leagues, stadiums, superstar athletes, etc. – its all there.
This mindless fanaticism with blitzball, at their own peril, mirrors the blind fanaticism Spirans have with Yu Yevon. Wakka is evident of both. And religion has turned us vs them, the religious vs the heretics, into a type of sport with opposing teams. And with all of the religious symbols and gestures, Blitzball is “like” a religion.
Like in the real world, ya?
Religion and sports are all the people have left, and really all the people know. Sin ravages Spira periodically, yet people still play Blitzball. Even into the future, when Tidus should be saving the world, he’s playing a sport!
But there’s more, like Tidus becomes professional athlete turned coach turn General Manager of his own blitzball team. He has to learn how to budget, scout talent, sign up and compete in tournaments…all while Sin and Yu Yevon are threats. Why would any sport take up so much of one’s time?
And maybe this is what the developers are getting at. Of course, it’s just fun little minigame that makes sense with the lore’s world. But then again, it’s kind of fits how we see sports, at our level. Art imitates life.

Later on in Final Fantasy X-2, when the fighting’s over, blitzball incorporates technology. All the while several factions are competing for dominance in Spira. Perhaps the sport is still a distraction to placate the masses?
Good thing the sport’s really fun. I love playing Blitzball! I wish I were one…