What you're suggesting though is just change for the sake of change, and more like science fiction than fantasy. It doesn't make the game more fantastic or cool to have wierd creatures in place of normal animals, for no apparent reason other than personal fiat.
PCs:
"Oh, so the riding animals are
hreignkadts, and are something like giant lemure-camel-stegosaurs....? Um, okay....."
"So....I can't have a cat familiar? But there's a cat-monkey-pig-mantis-like creature that kind of substitutes for cats? Uh, I guess I'll take that then....."
"I want to get a hunting falcon for this event we're going to....what? No birds? So what is there? Bat-cow-giraffe-goat-snakes? WTF? Are those the things that attacked us a few months ago in the mountains? No? Those were the flying mouse-zebra-chameleon-triceratops-things? .......Alright, screw it, I'm done."
That's more like science fiction and an alien world populated by alien creatures. If you're going to go that route, why on Earth are you only going half-arsed and leaving humans, humanoid creatures, and human-baseline cultures/personalities/linguistics/etc. in the setting? There's no reason to replace all of the normal animals if you're keeping everything else around that makes it a recognizably human world.
If it looks like a duck, quacks like a duck, and waddles like a duck, then it's a duck. I don't care if it's actually a scaly horn-beaked three-legged one-eyed whatsit, if it's basically filling the same role as a normal animal,
then why for Pete's sake isn't just a normal animal that will be easily remembered?
*secretly wants a cat-monkey-pig-mantis* 