Obviously they are in all of the Fallouts, including F4.

But do they belong there, from the perspective of the basis of the Fallout universe?

AFAIK the Fallout universe diverges from our own, where the World of Tomorrow expected by the 1950s culture actually came true.

Thus the nuclear powered cars, laser and plasma weapons, powered armor, household robots, and so forth.

Then the World of Tomorrow had a 1950s concept of nuclear war dumped all over it.

Resulting in radiation-created ghouls, giant scorpions and ants, among other things.

Does anyone know of any books/movies/stories from either the World of Tomorrow or the 1950s ideas of events after a nuclear war, featuring Super Mutants?

Otherwise, why are they in Fallout?

Things are not necessarily tied to their "basis" like it's religious dogma. Once a sequel is in the works it is merely necessary that it should be divergent from it, it becomes the new basis. As-long as subsequent installations to the world fit within it's establishment then it's fine.

But Fallout 1 by itself? The pulp stories of those days believed that radiation would create mutants; that is the sentiment from which the Super Mutant was created though layered then with a dark persona and, of-course, some necessary original creations for their existence in the universe.

Super Mutants are perfectly retro. Why are they perfectly retro? I'll tell you. Look at the history of FEV and what it was designed to do. Super Mutants are the unintentional failure of FEV's production. The FEV was originally intended to create the perfect super soldier. Stronger, Smarter and faster than the enemy, not to mention durable in combat. Super Mutants are all failed super soldiers. They may not be all Pre-War, but their dipping turned them into the failure results of FEV's intended goal. They're a horrific distortion of the Captain America dream.

Morlocks, or a variant belonging in almost every post apocolypse setting is a tribute to H.G. Wells