Up to the point of Zanarkand, it seemed like they were just 'the group'. After that, you could see certain people taking the lead. After defeating Yunalesca, Tidus motivates the group to try and find a way to end the cycle. Kimahri comes up with the idea of asking Mika, the fayth tells the group about Yu Yevon. Thanks to Wakka, Rikku and Lulu's idea involving the hymn and Tidus being onboard, Jecht allows the party to enter Sin's body. Yuna summons the aeons and performs the sending at the end.

I think if Tidus hadn't been there, the group wouldn't have had the strength or motivation to keep going, to look for a way to end the cycle. He really becomes the source of hope / motivation for the party. Rikku couldn't have done that had she been by herself.
Thinking about it, Tidus is really the only person who advises the characters, mainly Yuna and Wakka, to think about why they believe in Yevon and actually think for themselves. He was partially the reason for Auron to continue his existence, although admittedly, he probably would've anyway for Yuna's sake.
So yeah, basically, he's the guy who gets most of the party to not just accept everything around them like it is, but actually act to fight the problems of the world.
That and he has the Haste spell.