It's going to take more than a spell to make BST group friendly, though one along the lines of which you're describing would help. But that assumes another player would want to cast it on our pet, and we arrive at our previous issue of "BST is the Boogeyman and therefore should not even be in our group w- oh god my hair is on fire~" which is likely to prevent an invite in the first place.
I agree what I am asking for here is only a start, but I'd hope it would be one of the many considerations to take into account for transitioning BST into group play. So far, our only selling point is Snarl to make us a low maintenance damage dealer. But that amounts to very little against NMs that deal powerful Area attacks or that would wipe our pet in just a few swings.

It would really take many ideas that have been suggested countless times to in order to fix BST. Even things that are just on the convenience level like zoneable pets.

But we do have pets that are capable of healing Area Cure IV-V amounts. We do have pets that are capable of inflicting 50% Attack Down. We do have pets that are capable of inflicting Accuracy Down. We have pets that give us Treasure Hunter. We do have pets that can deal elemental damage. We have pets that can inflict Area Sleep. We have pets that can Stun, Dispel, and inflict heavy Poison damage. We could expand on Lulush's Wild Carrot idea and make Anna's Secretion grant Evasion Boost to the NIN or THF tank.

Behind all the annoying limitations is the potential for a very flexible job. But until we can let go of all the crap, none of us this is ever going to see practical application. Only a few steps up from what Sic used to be and all we could do was pray Carrie didn't use Bubble Shower. Really, shouldn't the fact we have to pick which pet we want to use on a strict Call Beast timer a limitation enough?