I think the issue is that people want a Beastmaster Job to play a Beastmaster Job. Not to just run around with a reskinned Chocobo (Since, Chocobo can already be Tank, Healer or DPS. If you're rich enough you can level it to level 20 and max out all 3 trees to boot)

Think something akin to Beastmastery spec'd Hunters in WoW, or White Lions spec'd for either their Lion or their Hybrid tree from Warhammer Online. Where you have skills that make your pet do something with you and have buffs you apply to each other.

As far as taming and the like goes... They could go the WoW route and put pets into different "Families" so that they can be grouped into similar stats/skills and make "Taming" more of a cosmetic change than actually core gameplay (Such as in prior games where you'd control an enemy in a fight for a short while, such as a single turn)

Alternatively, they could make Taming simply a side-activity, much like BLU going around and learning spells for such things as pure cosmetics or to utilize for such things as your Companions suggestion. While actually combat-wise playing more like the Tamer from BDO where the "Pet" is a shadowy/aetherial animal that comes out with your attacks. (This would also be able to bypass the crap AI that plagues SMN)