If Norman is going for realism this would severely limit what animals can be domesticated. Many animals are wild and have a mean or stubborn streak that prohibits domestication.It seems that the type of pet is more important than the amount of interaction with the pet, you could do a kind of Pokemon thing where players attempt to capture and tame powerful animals for their abilities.well, pets reduce the chance of being surprised by encounters, and they are another NPC follower you can give combat orders to.
This would go well with a hunting mechanic as it will force the player to decide: Will they kill the mammoth for huge amounts of food and other recources or tame it, for transport and a war beast.
A good real world example is horses vs zebras. They look the same but psychologically they couldn't be further apart.
Those animals could be tamed but never really domesticated e.g. you could perhaps have a mammoth learn that humans = food provider, but would they fetch, hunt or guard your camp? Not likely...
I was always told the simple rule "if it's in your house or garden it's domesticated and if it's in a circus it's tamed". There are still gotchas to this though. We have a bearded dragon lizard at home which is very much domesticated and a snake that obviously is only tamed.
If it's not obvious to the player what they can domesticate successfully before they try it could lead to some interesting emergent Gameplay...