I feel like there is already some bare-bones form of this in the game, aka squadrons. While I know you want something more akin to fantasy football, hear me out.

The squadron system does ""technically"" have stats mechanics and the ability to choose which style of tactics they use in battle (from offensive to healing, etc). There are also training regimens for it to increase and decrease general stats before sending them out on missions. There is also the option of using them for levelling your character by running dungeons with them. (You can also choose who you want minus Viera and Hroth...which is a result of neglected content. But you can also customize their appearances in later tier unlocks.)

Squadrons have been sorrowfully ignored and a revamp to include setting them up against other player's squadrons could be an interesting concept to elaborate on and, maybe, give the ignored content a new breath of life. (It'd feel in a similar vein to the battle in the HW patch between the GCs or PVP. Either way, it feels like there is something there that could be pulled for creating a version of "fantasy football" / Blitzball lol.)