I liked tetra master more then blitzball, atlast you got a nice card collection. anyways there were some perks with chocobo breeding.

1. You get good materia like mime, which means you can mime magic, summons, and commands (including 4 time cut, slash all, and even limit breaks), you get quadra magic which allows you to cast any spell 4 times (8 with w-magic) great with comet 2. Then there's the hp<>MP materia which can allow you to never need a ether ever!! when your low on mp say, 8000 hp 10/999 mp equip the materia that will make 10/999 hp and 8000/9999 mp. heal hp and take off the materia.

2. you can play the chocobo racing game. Along with gaining all the items you can win = worth doing. if you wn so many times on S rank you get a hellalota stuff for free. not to mention all the gp you can gain during the process.

3. You get knights of the round which can own Sephiroth as well as most bosses. If it don't kill them it will get close enough.

besides all that its fun to see a chocobo who can climb mountains, cross rivers, walk in the ocean and even walk without fighting a battle. fun times it is.