I could see leveling your monster just like it works in FFXI, then maybe have some PvP / tournament like"Touchandfeel" suggested above.
And wouldnt it be cool to go primal fights / raids as a monster ?

Ofc, if they did this for FFXIV, it shouldnt be less diffrent or changed too much or people woul loose interest.
Instead make it more or better than FFXI's version, maybe even more diverse / versatile.

Cool things about monstrosity in FFXI:

* You could name your monster.
* You could level it & select skills.
* Many monsters to unlock & select.
* Battle wasnt bound to a few pre-determined areas.

There could be alot of new cool content with this, if SE decided to do it.
And hopefully do