Console APIs are nice and clean compared to Vulkan though, since they are tailored to the underlying hardware. Vulkan is a weird compromise between a low-level API and covering fairly different GPU architectures.
The point was more about general APIs like threading or file access, anything covered by POSIX.
It is already expected to have to rewrite your GFX backend anyway using the specialized API for the platform, but people don't expect the same for general use APIs too.
Well, tell that to game developers working for consoles. They don't have access to the same APIs and they made it work just fine. Most of the time, you don't make your own engine and rely on some other engine to support your platform, so it just works.
I've done enough Wii, PSP, PS3 or PS4 development and having different APIs was never a problem.