The problem with fog is the fine water droplets in the air have a tendency to reflect incident light back along it's incoming trajectory, rather like a cats eye. And that's why headlamps especially on high beam tend to white out the drivers view as the lights and drivers eyes almost share the same axial alignment.
Traditional fog lamps were usually set lower than the head lamps to reduce the amount of reflected light. HGV drivers who tend to sit much higher than the headlights often had a better forward view than car drivers in poor conditions for the same reason.
Also it was thought that by adding a yellow filter to the fog lamps improved their penetration through the water droplets, but I think this has been debunked.
Similarly some people have suggested using polarised lenses to reduce horizontal reflected light. I'm not sure about this one.
I have not needed to drive in fog for many years I am pleased to say. I well remember thick fog and using old tungsten headlights with the reflection of the fog you outline. It is not nice.
I do wonder if modern halogen or LED lights would be better or worse in the same circumstances. Worse I imagine. Therefore low level fog lights would be useful. If used without headlights.
My own car, a Mazda C5 used to have fog lights, but Mazda have dropped them. I don’t know what Mazda’s reasoning is. Perhaps just cost saving. My car has the automatic LED headlights. The beam is constantly adjusted depending on what the forward facing camera sees. In the dark they work very well, though it is disconcerting to drive with the high beam warning light lit.
I do wonder how these will fair in fog conditions.
Any light that makes you more visible or helps you to see better is not an "ornament" is a safety advantage.
Except, I remember driving past a crash scene at night. All services were attending and every vehicle left their blue lights on. Could have been 20 vehicles there. The weather was fine drizzle.
The result was, oncoming traffic could not properly see the road or any diversions. The emergency services were inadvertently causing dangerous driving conditions in the area.
The affect was similar to following someone with rear fog lights turned on in rain, on an otherwise clear night.
John