To get a max power pet on the field, you currently need Creature Control and Advanced Creature Control. (Up to 200 Primary points)
To tame pets yourself instead of buying them or getting them from an alt/allies you need taming. Domination also works if you don't want to trade pets to others, though currently all it gives that taming can't is a crab. (Up to 100 Primary points)
To level them more quickly you need animal care. (Up to 100 Primary Points)
To have two or more pets herding is advisable to reduce the penalty (Up to 100 points but only 91 of them do anything)
You can heal your pet 30-50hp with a bandage. To increase this by 10% of the pet's HP you need veterinary. Very optional, especially if your build already uses magic. (Up to 100 Primary Points)
To do anything with beasts effectively, you need the Zoology for the type of pet you are using (100 - 400 Profession Primaries)
Beast Mastery and Beast Influence currently do nothing.
So to effectively use a max level pet you need most of 200 primary action points (Some top tier pets require slightly less than 100 PP to control) and 100 primary profession points. (CC, Adv. CC, 1 Zoology.)
To take all useful combat-relevant skills you need 391-491 action points and 400 profession points. (CC, Adv, CC, Domination*, Veterinary, 91 Herding. Mamallia, Reptilia, Anthropoda**, Aves. )
*This is the reason I say 291-391 as domination really is not advisable for most builds and never will be if it stays a sub-skill of Ecumencial.
**Domination only. Tamers and those using tamed pets do not need this.
To be fully efficient at taming and leveling pets instead of purchasing them from others you need 591 action points and 300 profession points. (CC, Adv. CC, Taming, Vetrinary, Animal Care, 91 Herding. Mammalia, Reptilia, Aves.)
Kind of like archery, I agree that a deep dive into taming perhaps should offer more value. But I'm sure you can see the 200 action 100 profession splash gives A LOT of value currently.