Though I suppose to make everyone happy you could just make all Exotics become a Skill based family. Have a quest or a drop from a rare/raid boss that ties into what the family is all about. Devilsaurs/Pterradoxes/Direhorns from the Zandalari NPCs, Corehounds from Molten core, and so on. That way you could experience some lore that ties to what it means to be able to command this specific family, and command it with any spec.
I'd really like that, giving a quest for every family currently in Exotic with a bit of backstory, or even just looting an item like currently for direhorns and the crawg beasts. Maybe having to fight some master trainer of those beasts (a Salamander NPC in the Firelands for the corehounds? A ghost for the spirit beasts?) until they have to talk/give lesson item if we don't want it to give too much work to the Dev to implement that. (Also I really want to keep my Loque'nahak with me no matter the spec...)
Right, so currently are exotic: (I'll throw a few ideas on how it could happens)
Chimaeras (Rylak & chimaeras)
Zone: Ashenvale (Alliance) or Frostfire Ridge (Horde)
How: Quest with a Night elf/Mag'har orc giving you instructions on how to bond with rylaks/chimaeras? Or maybe just a night elf, who recognize your deeds and care for animals even if you're Horde.
Details:
Alliance- A chimera rider of the Black Moon army is taking care of her companion as you visit the clearing. She tells you about the cry a mother chimaera makes for her hatchlings and how it get the attention even of an adult, and that they love [x kind of meat] and if you brought them some as a delicacy you can earn some measure of friendship. But never make that whistle, they dislike that.
Clefthoods (clefthoods & rhinos)
Zone: Outland Nagrand
How: Quest with a Mag'har orc telling you about the shared history of orcs and clefthoods, the cycle of nature and the hunt, etc.
Details: An old Mag'har is waiting at a campfire, and tell you all about the hunts they add in his youth, and the majesty of the clefthoods herds that roamed Nagrand, and how it's not like it was. If you listen to his entire story, he tells you about that young hunter he knew in his youth who adopted a baby clefthood, and taught it how to guard the village, and that surely the experience could be repeated. He goes into details of what that hunter did to let the little clefthood be used to people, and by the end you have the competence (based on your previous experience as a hunter) to try as well.
Corehounds (corehounds and cerberus dogs)
Zone: Firelands (not raid)
How: A Salamander houndmaster rare, who drop an item [Notes of the Houndmaster] that teach the competence.
Devilsaurs
Zone: Nazmir
How: A renegade Zandalari beastcaller rare (so it's doable by both Horde and Alliance), who drop an item [Prayer of Rezan] that teach the competence.
Krolusks
Zone: Voldun
How: A Sethrak rare, mounted on a krolusk, who drop an item [Krolusk egg] and maybe a small quest of observing the baby krolusk to teach the competence?
Pterordaxes (Zandalar and Pandaria)
Zone: Isle of Giants
How: Adding them to the Dinomancer tome? Adding an item [Pakurai prayer]?
Stone hounds
Zone: Throne of Thunder (raid)
How: Iron Qon drops [Hound book] (It's a bad name, I'll think about it more)
Shale spiders
Zone: Deepholm
How: Quest with one Earth Elemental in Therazane throne, teaching you about the little pests that are the shale creature but that they are also parts of the cycle in Deepholm and can be useful.
Details: The Earth giant wants you to get rid of some Shale worms next to the throne, and lend you a little flock of shale spiders to do it, so they'll hunt the worms with you. As he have to explain how to direct the shale spiders, he also teach you how to tame your own the next time you'll visit Deepholm.
Silithids
Zone: Silithus
How: Quest with a friendly-ish Silithid, leading you to bond somewhat with part of the hive mind. Or teaching the hunter how to reach the hivemind.
Details: The Chronicler escaped partly the bonds of the hivemind, all to its purpose of chronicling everything that happens to the Quiraji Empire, and miraculously not dead after the recent fall of the Black Empire. It charges you with bringing it fragments from the obelisks in Uldum, and in trade teach you how to read some of the runes, and some of those allow to reach the Silithid hivemind yourself.
Spirit beasts
Zone: Crystalsong Forest
How: An elven ghost gives you a quest to teach you how to open your mind to the Veil between this world and the Shadowlands/Emerald Dream, and how to bond with the creatures not quite from this world.
Details: The quest includes acquiring Spectral Dust from other ghosts, and sacred bones from the vrykul shamans of the nearby regions, and it concludes on a ritual, giving you a vision of the friendly ghost's own companion and their blessing to bond with other spectres.
Water striders
(I never realised they were exotic, to be honest)
Zone: Zangarmash?
How: Friendly Sporeggar people gives a quest on how to tame the striders of the zone.
Details: The quest includes getting some specific spores from plants of the zone, and the sporeggars teach you about how those ones specifically calm down a strider, and those other ones will make it aggressive, and these will help you bond for they are not quite social creatures.
Worms
Zone: I don't know, I've no idea why they are exotics and the wasps are not. I'll think about it more.