Makes a ton of sense for cross-platform, and also Vulkan appears to be better than DX12 at the moment. Both in performance and stability.
Also if all the consoles start using Vulkan (phones do, and the PS4 uses/used OpenGL so I assume they're switching too), then pretty much everything would run it.
In a perfect world yes all platforms would support vulkan. Issues is i cant see that happening in the real world :
* Xbox One uses its own "close to the metal" DirectX variation that is made to take advantage of the console HW (i think its almost a DX11 / 12 hybrid)
* PS4 uses a variation of OpenGL thats optimised for the HW as well
I cant see the console makers retooling their development kits for little to no performance gains. You also have apple who use their own metal API.
That being said having a fully cross compatible API for windows / linux / android covers a very large number of devices