Alot of em can write and rap, in fact any rapper who cant write for himself aint no rapper at all (one thing to occasionally use writers, like Snoop done), Dre himself basically says he aint no rapper. Adding production to it is another matter, but there are a few, like Big Krit for example excells at all 3.
And your obbsession with MF doom is charmingly amusing

(he is better producer then the other two though for me, very specific type of boom bap beats). But yeah Operation doomsday is nice.
About MF doom, corious about a collabo work he is doing with a kid he is mentoring called Bishop Nehru. Should be nice.