This is simply not true. To begin with, the shader languages and bytecode formats are different across OpenGL and Direct3D. Consoles tend to have their own shader pipeline as well. Even if you have great abstractions in your middleware, the capabilities actually provided by the system differ, and you have to consider this. APIs and drivers remain extremely relevant, middleware or not.
FWIW the PS3 (among others) actually offered OpenGL, not that you'd want to use it (the implementation was pretty bad - Apple-quality).
You can also theoretically run OpenGL code on the PS4 or XBox One if you want to, since they use well-understood AMD GPUs. Fail0verflow has already booted real OpenGL on hacked PS4s (via Mesa, I believe).
You can also run OpenGL on some platforms by using ANGLE to emulate specific versions of OpenGL on top of other APIs.
So, ultimately the "there is no OpenGL or Vulkan" observation isn't that meaningful - if your codebase is built around OpenGL, that's not necessarily a problem at all.
I don't know if I'd bother, but I'd also put money on it being possible to run ANGLE or Mesa GL on top of the PS4 graphics stack (I'm familiar with it).