Why did Zeus sleep with Persephone?
This is a great question. And it leads us to the problems of ancient myth. Persephone is a vegetation and underworld goddess that hails from several different strands of traditions. Some scholars believe that she is Mycenaean in origin, but her appearance in the Orphic mystery rites probably descends from an Egyptian source. The cross cultural ties between Mycenae and Egypt are probably more prolific than understood. So once again when looking at the various stories of Persephone be aware that they are an accretion of several different forms and sources.
In the Orphic tradition Persephone was seduced by Zeus in a cave guarded by dragons and gave birth to Zagreus, who is often compared with Dionysus. Orpheus and Dionysus are often homologous in their functions, and Dionysus repeatedly shows up on the Orphic gold plates found buried with the initiated dead.
According to the story, Zeus impregnates Persephone before Hades abducts her. She gives birth to Zagreus/Dionysus, who is then torn into pieces by the Titans and his body parts are thrown into the river. Athena retrieved his heart from the river and gave it to Zeus. Notice how similar this is to Osiris being killed and his body being cut up into pieces and thrown into the river where Isis retrieves his phallus. While the retrieved body parts are different, their functions in the separate cultures are similar, as the heart/phallus was a symbol of life and birth.
Furthermore, the name Zagreus refers to a hunter, and this god-hunter held keys to life and death. This may correspond to the constellation Orion, the great hunter, who was Osiris in Egyptian tradition, Dumuzi in Babylonian tradition, and probably represented Orpheus and Mithras as well. The hunter catches wild animals, which is symbolic of the crude mortal human who has not received apotheosis or divine blessings. Lucius is turned into an ass and can only return into human form by being initiated into the mysteries of Isis. Gilgamesh, Heracles, and Orion all rape or destroy and must go through a series of labors which always ends with the secrets of rebirth. This is a strong theme of hero cults associated with some form of rebirth.
It may be that Zeus impregnates Persephone as a way for the Greeks to acquire the funerary aspect of this goddess. Zeus, through the rape of Persephone, makes an Egyptian source turn into a Greek custom.
Again this is speculative, but it is these kind of connections that inform the origins of the myth.