[Erik]

"What are these situations?" - Too numerous to list. Any time the lighting is such that the sights are difficult to see superimposed over the threat/target. Both parties could be in low light; the shooter may have entered the shadows from the bright day light creating the impression of low light others already inside do not perceive; the threat/target could be in well lit conditions and the gun in poor ones; etc.

"Should a person be shooting at distant targets in the dark?" - The threat does not have to be distant or in the dark (see above). Many train to get on their sights quickly, and the threats/targets need not be defined as "distant." But, in low light tritium sights afford the ability to register them much faster under low light conditions.

"How likely is someone to face this decision?" - Likely, should the need to defend yourself with a firearm arise at all. But, the idea is to prepare yourself, and afford yourself the ability through equipement and training to quickly register your sights and use them as needed across a broad spectrum of lighting conditions.