Yeah it would be cool, to take care and grow your pet, and after that to have the option to use it as a mount when it's fully trained.
Mounts with different skills (like in G.W2).
»spider/insects being able to scale walls.
»goats/cats may fall with damage reduction.
»lupines/canines immobilizing with tusks.
»bull/boar being able to run over enemies.
» dragons/bears stunning or frightening with a roar.
Providing a skill for the character to use in mounted combat