Limited Job #2: Beastmaster

[Kisshu]

FFXI, similar to FFX-2 in that you could only have one pet out (though you could get multiples I believe) and the pets did the majority of the attacking. AI had control here for the most part, and the pet could grab aggro. Due to how the pet system works right now in FFXIV, I don't believe that'll be possible.

That's a major simplification of it. First off, BST got an A+ rating in axes which means they're the best of any jobs to use that weapon. So they can do a lot of damage on their own.

BST worked by you charming a pet in the zone and have it fight besides you, or that was the plan. But due to charm not always working, people fighting monsters many levels above them and pets not getting any accuracy/attack bonuses meant that the BST pet would either not do a lot(miss or weak attacks) or the BST would have to charm a strong pet(levels above the BST) but that would screw with the party's exp gain.

Those were some of the factors that forced BST to be a solo job, so they had to adapt. Pitting a strong, charmed pet against a strong monster and work in a way that the BST didn't get hit while killing the monster.
Later jog pets were introduced which were summoned, timed pets.

What you described above with the pets doing most of the damage is much more akin to the FFXI summoner than anything(and FFXI SMN had to go around to gather avatars to actually be able to do anything meaningful).