These spawnflags were inspired by Quoth 2 (Kell and Necros, 2008), which included two additional spawnflags for all entities: Not in Coop and Coop Only.
In contrast to Quoth 2, the spawnflags implemented here are Not in Coop and Not in Single Player, for symmetry with the built-in Not in Deathmatch spawnflag.
The set of built-in spawnflags doesn't allow a mapper to treat the Hard and Nightmare skill levels differently, because it only includes one spawnflag, 1024, which excludes an entity from both Hard and Nightmare.
The new Not on Hard Only and Not on Nightmare Only spawnflags allow the mapper to exclude an entity from one of these skill levels without affecting the other.
The original spawnflag will supersede the new flags.