They'd never make it, the least difficult road to making a job is picking something simple and close to pre-existing ones. So the only way bst would work, and this is what they would do if they did make a non-pet pet class... is to make their attacks work in various wild animals that show up out of the void.
Much like SMN should have been, with you summoning for example ifrit's arm or garuda's wings or something to do an attack out of a void an animal can just show up with certain attacks and attack it in a predefined animation with the animal that does not actually create a npc.
Basically, something like stampede/stomp in wow for their BM spec.
In all honesty, if the devs can't even think up an interesting work around like that it's not surprising they're afraid to make a true pet class or have trouble with their current mistakes with one.
Meanwhile wow has a demon summoning spec that summons like 8 pets, lol.