If you look carefully it's surprising just where lesser-known mythological figures like this tend to pop up in places you wouldn't expect them.

I mean on top of the very broad idea of the immortal bird of prosperity being also a pretty ubiquitous concept in our folklore the world over, there sure is something about a whacking great bird with pretty colours being associated with the human fixation toward death and rebirth. No wonder it fits right in with Pokémon's distinctly shinto-buddhist-leaning view of myth as a narrative feature.