I know that document. It doesn't really answer this point though. It motivates the need for parallelism in slow python by noting that this is important once other performance critical code is in extensions.
But the mai point against multiprocessing seems to be that spawning new processes is slow ...
That single "alternatives" paragraph doesn't answer at all why mp isn't viable for python level parallelism.
I am no longer invested in python heavily, I am sure there are discussions or documents somewhere that go into this more. Might be that it's simply that everyone is used to threads so you should support it for sheer familiarity. All I am saying is it's not obvious to a casual observer.