People said the same about WebGL. Today Microsoft is a member of Khronos.
Vulkan can be implemented on anything. It's just a matter of performance. And since Microsoft defines DirectX, they can add any features they need to improve the performance of a Vulkan implementation if they so choose.
What are the issues with Vulkan-on-DX12? Metal is missing geometry shaders and the tesselation shaders are kind of weird, plus GPU heap allocation is iOS only so I understand the difficulties there (although as kvark mentioned there is a decent Vulkan-on-Metal implementation for the rest of the API in the works). AFAIK DX12 has all of that.
Also Windows GPU drivers already support Vulkan (all the way back to the 600 series in Nvidia's case IIRC), so I don't see why that would be a technical deal breaker. And it definitely won't be a "political" deal breaker for Firefox or Chromium on Windows.
Vulcan cannot be implemented on top of DirectX12 or Metal.
So it's never going to happen.