When i hear things like 'chocobo only' ' beastmaster' i can only shake my head...

it would not hurt to have otehr mounths.
Use your imagination, there could be mounts that you permanently own and mounts that you rent,
Imagine riding a magictec armor like in FF6, how cool would that be...

Beastmaster is in no way a good substitute for what people call a 'pet' like in other MMO.

It would not hurt to have little pets, that would add some nice touch.
They don't have to be large tiger and they don't have to participate in battle at all.
Everything could work great if well done.
Well if you don't ride a choco then it's not an FF.
Although I am 100% supportive of trying new stuff on new games, this is one of the few things that I don't ever want to see changed in an FF game.

Also Beastmaster is perfectly "ok" for a fighting pet class.
He can get as pet about any monster in the game and he can have his own pets too.
Also summoners and Dragoons have "pets" and they are both fighting classes too.

If by the definition of "pet" you mean to take a little monster and rise it then this have been done too with chocobos.