Actually, the minotaurs are weird because they have two explanations. They're in Elpis, but the Encyclopedia Eorzea also credits them as specifically a third-generation chimera made for security detail. There's a few other creatures in similar situations, too.
Personally if I were trying to square that one, I'd go for 'the Elpis animals didn't survive for whatever reason (not even necessarily a big reason, animals just go extinct sometimes), but Allag reinvented them'. Even outside of situations where they conceivably could have come up with a similar idea completely independently--'existing thing but with wings' doesn't exactly require great leaps of creativity--you can point to Amon's dreams of Elpis as a potential bridge.
I wouldn't want this in any way at all, because it actually devalues and demeans the tribes that we're told envisioned and believe in these figures. 'All of these tribes simply misunderstood a creation made by the effectively-perceived-as-human Ancients' sounds really bad, and basically strips them all of any agency of their own on a societal level. I'm already not a big fan of the fact that Ifrit was entirely explained away as an Ancient creation in a short story that isn't even in the game itself.
Bismarck works and makes sense because the Vanu Vanu's belief system and culture is very totemic and animist; it makes sense that they ascribed deific abilities to an animal they saw do a thing, because that's the sort of society they actually are, and even then they don't really worship Bismarck as their creator, that's not his role in their stories, they see him as the creator of the Sea of Clouds. That's not true for a group like the kobolds, who not only ascribe their own creation to Titan, but whose society is more rationalist and not the type to elevate external things in that way.
And it starts to sound REALLY bad when you factor in the Twelve. "Oh, all these other religious beliefs are just their people misunderstanding something entirely normal, but the majority religion of the place you call home? No, their gods are completely real and pretty much exactly as they say!"
EDIT: Centaurs, to answer the OP instead of just handwaving vague 'probably Ancients' non-explanations, are also explained by the Encyclopedia, but it's a little weird; in the game 'centaur' is specifically used to describe a type of Sharlayan construct, but as we all know there's been a few other creatures of the same shape, some artificial (Reptoids, the Ultima Weapon), some not (the society that summoned Zurvan). So I think it's just a reasonable explanation that centaurs as we understand it are just a thing in FFXIV's world, it's a good shape that both nature and man keep relying on. Or you could say 'it was the Ancients' and throw away everything else, I guess.
If you're ever unsure about why a monster in the game exists, and it's in a part of the game before the late Stormblood patches, I recommend just checking the Encyclopedia Eorzea, it usually has some ideas. You want an explanation for the Skatene? That's in there, turns out those were Sharlayans' fault! We don't have that resource on anything past about 4.2, but with the third volume being worked on, that problem's days are numbered!