Coincidentally, one of OUYA's featured games right now is a Final Fantasy title.
True, it's probably more like the original X-Box in that regard, which also had no established franchise exclusives. It also didn't make money until towards the end of its life cycle, while Microsoft threw money at it in the meantime.
Obviously Julie Uhrman has thought about this, which is why she's made deals with people behind games like Portal, Papo & Yo, The Ball, Journey, etc. to make exclusives. They're not Final Fantasy of course, but it might help build momentum and attract more developers.
That said, I don't see the OUYA library ever offering anything that will make anyone buy it because they just HAVE to have that game. On the other hand, I do see it potentially becoming the preferred platform for devs who want to port their PC and mobile games to console and don't want to expend the time, effort, and resources to put it on one of the big 3. So over time it will build up a collection of games that will be exclusive to it in the CONSOLE space. You'll probably never see Final Fantasy III on PS3, so if you want to play it in 1080p without touch controls blocking the screen, OUYA is the only way you're ever going to be able to.