I've seen beds in super mutant outposts in Fallout 3/NV/4, but never seen a mutant occupying one. Is this simply because nobody wanted to give them the necessary animations and scripting, or is there an in-story reason they don't sleep, possibly explained in Fallout 1/2?
There is no "real" reason why super mutants never sleep. However, this might be caused by the F.E.V which infected them. One of it effects is that cells regenerate in such a high rate that they can't die a natural death. So I suppose - I just suppose - that the F.E.V is altering them in such a way that they don't have to sleep.