Do you happen to be familiar with ANGLE? What happens if I just expose GLES 3.0 bindings as WebGL2 based on the native drivers on each platform?
(my earlier understanding was that ANGLE was a WebGL-to-Direct3D translation layer, for compat on Windows.)
In addition to all that, it does let you use DirectX on Windows instead of GL (and Metal on Mac and Vulkan wherever). The reason you want that is that many Windows PCs do not have a GL driver installed. Microsoft does not ship one, so if the OEM didn't install one and the user didn't install one then it simply doesn't exist. And even when the GL driver is installed, it is often buggier than the DirectX driver. Similarly on Mac, GL is buggier than Metal (and officially deprecated).
This is somewhat less true than it used to be since one of the required features of OpenGL 4.3 is GLES 3.0 compatibility. Unfortunately, Mac OS is stuck on GL 4.1 forever (at least until they drop support completely anyway) and the other points you bring up are quite valid.