https://en.wikipedia.org/wiki/Vulkan_(API)#Compatibility
In addition to Nvidia and AMD, Intel, Imagination Technologies, Qualcomm (!!!), and ARM support Vulkan. Hardware wise, there is absolutely no problem whatsoever.
The current Plan Of Record is that Intel® is not supporting Vulkan on Windows drivers. The drivers that were made available on Developer.com are intended for Vulkan developers.
So, it is expected that some Vulkan drivers may not work for end users.
Intel GPUs power at least 50% of Windows PCs, and I'd guess the number is closer to 70%. Unless this situation changes, Vulkan is not the single cross-platform answer.
"Vulkan support right now is for 6th Generation and newer products and we are targeting developers not consumers. Thus why the releases are beta and are listed in the Game Developer Zone and not anywhere else."
is full Vulkan support planned for consumers: "To my knowledge yes, but I do not know when and would not want to hazard a guess"
Windows 10 is at around 25% currently.
https://en.wikipedia.org/wiki/List_of_games_with_Vulkan_supp...
Versus these ones:
https://en.wikipedia.org/wiki/List_of_games_with_DirectX_12_...
The fact that game studios decide to use one API or another is no factor in evaluating API availability. (Also note how many DX12 games not published by Microsoft are DX12 exclusives - that says something about Microsoft motives, but not about API qualities).
When given the option, professional game developers choose the one that better helps them achieving their goals.
All of them used by most desktop applications on Windows, including image, video and 3D editing applications.
CAD, GIS, or other applications that need to use 3D explicitly, on the other hand.... Basically only Autodesk ventured there, with 3ds Max and AutoCAD (since 2015).
For example, most of our customers prefer MicroStation, for some reason (no, we are not Bentley shop ;).
And actually, by the numbers there are more titles on Vulkan than there are titles not released by Microsoft on D3D12.
NVIDIA and ATI are hardly "all" vendors I care about. I'm personally not interested in the big desktop PCs. YMMV of course. But I'm personally very against "winner takes it all" and I'd really like some more universal web API, especially one that consumes less power on the iOS devices.
Edit: the answer to the question below by sydd: I'm honestly and pragmatically interested in iOS and Apple devices, not Microsoft, and not the Google-controlled ones. All these comments are about Apple's proposal for a standard for Web. I'm with the ones having the smaller market share here. I'm still sad Opera Presto is no more. I consider such "smaller" players extremely important for the web.
Also "Vulkan is available on all versions of Windows that are on DirectX 12, so there is potentially some value to the developer community to having a single API that spans multiple Windows versions."
Vulkan is fully supported on Windows with semi-recent GPUs (e.g. its supported by Nvidia with Geforce 6xx - released in 2012!) by all vendors.
The article is only saying that MS defers what API is supported to GPU manufacturers. Its not supported by Xbox and Windows Phones, but Xbox is a very different market and no one cares about Windows Phone.