There's no way that they would create such an influx of mounts in the game. Not only would it flood the roster with "similar" mounts, but they'd really lose the opportunity to make them actually have a meaning behind them besides "I got lucky." It would also require a ton of extra work for every "tamable" enemy model in the game since it would have to scale with the races and the animations would have to be matched up with the rider's movements. The only way I see this being implemented is for the Companion system, which would replace your chocobo. Unfortunately, I highly doubt SE would put so much effort into a part of the game that can really only be used during solo play. Besides, even if they did, who would honestly put hundreds of hours into leveling up a second companion?