Microsoft plays roughly the same role a Khronos (specifies the API, provide conformance test suite, provide an SDK, etc.) but when it comes to actually “shipping” DirectX, Microsoft doesn't have anything to do either, it's all on the graphic card vendor to ship DirectX drivers. As an example, for a while after its release, many people didn't have access to DX12 at all, just because their GPU didn't have DX12 drivers.

So the situation is much less different between DirectX and Vulkan than you make it sound.