Gameplay-wise, some games this technique will not work for. For example, say you have an indoor or outdoor environment where you have game assets that you want to have distance fog appear on top of, if the game player can move relative to those assets in such a way that you would want the distant fog to disappear, then pre-baking it will not work. But if the distant fog only appears on assets that are always going to be far away and the player (camera) can't get closer or farther from it, then you can prebake the distance into the vertex of the asset. This pre-baking could be done using vertex color, or even texture UV. Then in the material for that asset, you would use this distance information from the vertex color or texture UV to create a distance fog like effect.
The fewer operations the material has to do, the better. So one of the cheapest ways to do pre-baked distance fog is when the distance fog and asset color is combined to form a single gradient, which means that an unlit opaque material just need to use the distance information as the UV for a single texture lookup.
If the query is about how to pre-bake it. If you are using UE's Landscapes, I do not have enough experience with them to know how or even if it is possible. But if you are using a procedural mesh component, then you can put the information into the vertex color rather easily, but you have to either programmatically define the entire mesh, or open another mesh and then create a procedural mesh using it. I believe both UE4 and Blender have tools for painting vertex color, but I think for this purpose it would be rather tedious. You really want an editor only programmatic way to calculate the distances and store that with the mesh vertices. While opening several meshes and combining them into a single procedural mesh might sound tedious just to get distance fog, keep in mind that this will also mean you've just reduced the draw call of those meshes into a single draw call, which is kind of nice.
Personally, I think this is good technique for very distant geometry like far away hills and mountains. Things that are so far away that you don't need to worry about having trees or other objects on top of it. Things that are so far away that you don't need to worry about changing the fog because the player can't move far enough for it to make a difference. I think most VR Quest games I've seen don't go this route though, and instead just have texture backdrop.
