An engine failure in a single no matter how unlikely over extensive dense fog gives you no other options but to hit whatever is concealed in that fog.
Same at night
I don't disagree, but casting the first stone comes to mind. To acquire my various bits of paper I had to log some 10-20 hours at night, most of which was solid "no escape route" time.
I think I remember reading in the IFR test prep notes from the CAA that minimum cloudbase for the test to go ahead in a single is actually 1000ft (for enroute) - this seemed sensible to me so I adopted it for any SE IR that I do ...
The examiners can specify whatever they want. They also don't fly over water in singles.
The reality is that engine failures under the circumstances discussed barely feature in the stats. Most of the stats are packed with other stuff, like CFITs, running out of juice, mismanagement of the fuel system, loss of control following structural icing, airframe breakup through flying too fast into a CB, etc.
But only in a twin
You are fortunate in that the "JAA IR =
FTO" monopoly, at an eye watering £450/hour, gives you that option