By default, both Firefox and Chrome use the ANGLE layer to render WebGL draw calls under Windows. ANGLE is an implementation of the OpenGL ES 2.0 specification that is hardware-accelerated via Direct3D 9. So native OpenGL is not even used on Windows. I'm sure that it's possible to achieve something similar with Metal.
It seems like writing one OpenGL to Vulkan converter to rule them all would be the best solution. It would allow GPU vendors to focus on optimizing the much smaller and performant Vulkan
engine and would probably reduce driver size by a couple orders of magnitude.