Hm... story-wise, I felt it was necessary because, like another User had said earlier, it was sort of like the competition thing to win Zidane's attention, even though Garnet wasn't really interested. Plus, I think it was nice with the whole Extraction Spell that Zorn and Thorn cast on both Garnet and Eiko.
Gameplay-wise, I used Garnet much more than Eiko. I only really found Eiko useful when Garnet lost her voice and the message, "Command failed; Garnet can't concentrate" kept popping up, which was pretty annoying. In the end, I chose Garnet.
Really... I wasn't too bothered on the idea. Though, I like the idea of a designated Summoner(s) rather than have the whole Party being able to summon.