Except that's the thing. He's not annoying throughout the entire game; he grows up and matures as he realizes how things are in Spira. The only way he can really continue to annoy you past the halfway point of the game is if you don't like cheery, optimistic people. He goes from irritating and self-centered to completely selfless and loyal to his friends, willing to go to any odds to protect Yuna, and doing just that. That is a well-executed character, because you can clearly see these changes through the course of the game.
And that's why I love the ending of FFX so much - it's an amazingly beautiful, emotional ending, but it's not necessarily a happy one. It's very bittersweet. It's not the typical "girl and boy fall in love and live happily ever after" ending. There was no way for there to be a faerie tale happy ending in that game. And that is also part of why I'm no fan of X-2 (beyond Lenne and some of the costume designs), and will not generally acknowledge the existence of the good/perfect endings.
I used to hate Tidus. Haaaaate. However, looking back and thinking of how they told the story in the game, and how he did change...while he is not my favorite character still, they did do a very good job with showing how being in Spira changed him.
Yuna...she did mature eventually, and she did have a rather large stubborn streak, but it annoyed me that we're relying on someone to save the world, who has the backbone of a limp noodle and relies so fully on everyone else to make decisions for her. However, she did step up and mature and undergo some development and growth.
However, the best characters were the 'side' characters - Lulu, Auron, and Rikku. And don't even start me on how they destroyed Rikku's characterization in FFX-2...