It isn’t, and many do.
Autosetting the glyphs correctly is actually one of the requirements for a Steam Deck Verified badge and Steam supplies a library that has them all, so modern games are pretty good at it. And if you implement that, you might as well add a menu option to change “Auto” to “Switch” or “Playstation”.

There just was a quite long period where majority of games used Xinput thanks to Microsoft, basically only working with Xbox controllers, and as a response a whole bunch of controllers identify as Xbox controllers when plugged in.