I really like the idea of BST as a XIV tank, also.
I can imagine a BST tank in XIV meta something like so
1hander with a morning star main-hand, a off-hand padded cesti (like.. not a shield exactly, a monk weapon that covers the forearm - like some do), essentially a shield.
Charm 1 is their tank stance, Charm 2 is their DPS stance.
With a Charm I, a pet is summoned and 25% of the damage inflicted on the BST is redirected to that pet. The pet has an HP bar but cannot be healed by anyone other than the BST.
BST also has Command abilities that increase the percent of damage the pet will take (increase it from 25% to 45% [Rampart], increase it to 65% [Sentinel]).
Instead of waiting on Cooldown timers for defense moves like ShadowWall/Vengeance/Sentinel with DRK/WAR/PLD, the pet's HP bar acts as a pseudo recast for defense CDs. If you leave up BST's 'Sentinel' for too long, the pet could die or abandon you.
Also there are Loyalty stacks built under Charm 1, Feral stacks built under Charm 2. This incentives BST not to let their pet die also, as stacks are lost (similiar gauge mechanics of PLD/WAR).
The pet's HP being a sort of resource the BST can tap into, but throttle up the Pet's portion of damage intake for too long and he bails, he takes too much damage, he dies.. BST pulling a bit from DRK who uses MP to throttle productivity, but with BST it's based around the pet's HP. Of course BST still has traditional mitigation and role skills too to alleviate pressure off the pet mechanic. I think that would be a good resource mechanic for a pet tank job.
I started rambling on about a Job theorycraft. tl;dr BST tank would be awesome, and it's doable within the game meta.
Maybe not in the traditional 'pet job' way some people want. But we didn't get a trinity-breaking RDM either, the sky didn't fall.