One of the problems is that libraries consuming SPIR-V are generally not robust enough to handle untrusted web shaders. Also, DirectX doesn't (yet) accept SPIR-V shaders so you'd mandate some translation to HLSL, which in turn would be compiled by dxcompiler.dll
But writing an entirely new, bespoke high-level shader programming language is more robust? And robust in what way? The SPIR-V format is vastly easier to parse than a textual language.
And WGSL will still bounce through HLSL for DirectX because DXIL is an awful, undocumented mess of ancient LLVM-IR with a giant pile of bolt-on special semantics. Directly authoring DXIL is awful.