The big problem with that sort of AU, and probably the reason why it's not as popular (other than that it doesn't particularly lend itself to writing lots of D/s slash) is that it's not in and of itself a generator of conflict. People have spirit animals! Yay! Now what? The Zoo City version is better in that respect because getting a spirit animal by definition means that your character has done some serious bad stuff, and there will probably be consequences, but not everyone wants to write about an ex-(or current)murderer.
But it is fun making lists of what daemons you think that a given character would have, and considering facets that Pullman didn't address - as for example, men have female daemons and women have male daemons in the books, but would a gay man or woman have a daemon of the same sex? Would a trans person have a daemon whose gender complemented their physical body, or the gender they feel themselves to be? Are people with dog daemons really servile by nature, or is this just the classism of Lyra's culture talking? What do people do if their daemon settles in a form with very specific environmental requirements - like, what if you live in Cleveland, and your daemon settles as a Pacific salmon?
For Buffyverse characters, obviously vampires would have no daemons. Angel and Spike would get their daemons back when ensouled - but what about other types of demon? What about Anya? If Lorne had a daemon, would it be some kind of Pylean critter? If I were doing Barbverse Spike, what, if anything, would he have post-Mohra blood?
Angel = timber wolf
Anya = red squirrel
Buffy = cougar
Cordelia = peacock
Darla, pre-vamping = ermine
Dawn = ruby-throated hummingbird
Drusilla, pre-vamping = roe deer
Fred = Grisons Striped goat
Giles = Pharaoh eagle-owl
Gunn = Malaysian sun bear
Hank = beaver
Harmony, pre-vamping = Angora rabbit
Joyce = caracal
Lorne = the Pylean version of a scarlet macaw
Oz = dingo (which morphs into a wolf after he's bitten.)
Tara = vicuna
Wesley = reticulated python
William/Spike = English Bull Terrier. Which is part of the reason Cecily felt he was beneath her - he has a servant's daemon, how common. (In the Barbverse, when Spike gets brought back to life by the Mohra blood, he would manifest a new daemon in the shape of his Pylean demon-form - which is strongly influenced by the shape of his original daemon.)
Willow = Central American squirrel monkey
Xander = river otter
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