Vulkan is still an abstraction. Most PS4 developers I know would prefer the stuff they already have which is closer to the metal. Something that uses the actual instructions for the PS4 GPU and not some cross platform API that then has to be translated to the actual GPU.
Yes, PS4 devs porting to PC would likely like Vulkan over OpenGL or DirectX but PS4 devs on PS4 not so much.
Making games for only one platform doesn't make sense since it limits reach, and using tons of incompatible APIs is annoying as well. Vulkan is low enough of an abstraction to perform quite well, so no matter what direction something can be ported, having a common API can save a lot of time.
Yes, PS4 devs porting to PC would likely like Vulkan over OpenGL or DirectX but PS4 devs on PS4 not so much.