you will not solve any of that graphics problems with that fog shader to be honest. Those graphics problems are caused by the VR renderer and how good it utilizes AA and in which render resolution you render the original image. There are big differences between the hmd renderes. Like the one WMR is using, the picture quality is really good and such aliasing is not a big problem there, whereas with the oculus renderer there is a really bad picture quality in normal resolutions.
I just did a direct comparison between the HP Reverb G2 (WMR) and the Meta Quest 3 (Oculus - cable) and the "shimmer" or better called "aliasing jitter" is very minor in the G2 but huge in the Quest.
So sure fog could solve this, but only because you just have no objects / contrast in the renderer then.
One thing you can also do is gaining the mip lod bias. This will prevent high detail in those "line" or stait textures/objects:
Just an exaggerated example:
View attachment 1343954
So distant objects will sooner use lower mips and so the textures become more blurry and the aliasing jitter is therefore way lower.
Another fog solution you can do is lower the fog distance of the track then, like here in Pure Config:
View attachment 1343956
When gaining the FOG_SHAPE, the AC fog gets less distance and will so mask such objects, but with all resulting visual downgrades in view distance.