I see people trying hunter's build already, which means archer/fighter in heavy armor with battle pet. Making domestication tree a proffesion would destroy any balance that is left. Everyone would run pokemon trainer cos it would be non-brainer best option to do. Especially when zoology tree was moved to proffesion skilltree already.
No-one is saying move the domestication tree to profession, all people want to be moved is taming and animal care, as those aren't needed to have a pet in any way as you will be able to buy them just as you would a sword. You would still need, creature control, beast mastery, herding for multiple pets etc. and you could have the same build with or without taming and be no different in combat