> the advantage of being fully cross-platform

I would scratch the fully, it's not on iOS or macOS

Neither on any Android < Android N, or any console produced by Sony, Nintendo and Microsoft.
Sony and Nintendo have both announced Vulkan support on their next console iterations.
Sony historically supported OpenGL too, and approximately 0 games ever shipped with it.
Vulkan could very well be a different story, it doesn't have OpenGL's shortcomings.
The PS4 API is already much better than Vulkan.
> The PS4 API is already much better than Vulkan.

It's like saying that assembly is better than higher level languages. So propose writing everything in assembly as the next step? Everything has its trade-offs.

We don't really have enough experience to compare GPU assembly vs. SPIR-V. For pjmlp's claim that the PS4 API is "much better" than Vulkan to hold up, as far as I can tell you'd have to show that the codegen (i.e. passes after IR-level optimizations) of the driver's SPIR-V compiler can't match what game developers regularly do. I'm doubtful (instruction scheduling, for example, is too much to keep in your head to regularly beat a compiler), and especially so without data.
As I replied on another comment, besides the lower level control of pushing pixels around, there is the whole tooling part and OS integration.

Vulkan like OpenGL is leaving to the developers the effort to bring their own math library, OS integration and graphical debuggers.

For the rest most of it is hidden behind NDA walls, so you need to sign one to see the codegen examples.

Leaving math library and OS integration to developers is a good thing. Mandating them is already too limiting.

Graphical debuggers on the other hand are useful indeed. LunarG stopped working on Glave: https://github.com/LunarG/VulkanTools/commit/87220f80a643860...

Not sure what happened there. Valve were sponsoring Glave development.

Renderdoc is active (not Linux UI yet however): https://github.com/baldurk/renderdoc