During raids and dungeons, u barely notice your pet or its a liability. During outdoor and delve content its great to have a tanking buddy.
So my suggestion would be; give hunters a final tier talent that allows them to summon a pet that deals no damage, but keeps doing thread generative abilities (Like a voidwalker). And whenever your eagle deals damage, let it instead of dmg heal your pet.
I feel this keeps the fantasy intact, making your pet a range-support, still keeping bm unique, balancing dmg of the class for the given utility.