Why does Ishtar go to the underworld? [x-post from /r/mythology] -- any occult perspectives on this?

The same reason Heracles and Dante did. Death in mythology typically isn't about mortality, but what we don't like confronting in ourselves. When we pass through the gates to the underworld, we have committed to self realization beyond what we idealize. Heracles was initiated into the mysteries before he could enter, and Dante was guided by Virgil. Ishtar was only admitted by 'ancient decree', which is again - initiation. It requires commitment and sacrifice because we'd only be torturing ourselves taking minor excursions into the darkness and not returning with the prize at the bottom of the box. Making it through the nine gates symbolizes nine instances of being existentially disturbed and choosing whether or not to continue onto the ultimate truth. Compare the myth to how the tibetan book of the dead relates to the eightfold path.

The top comments on that page are pretty solid. Another persistent aspect of the myth is belief that the initiate to the priesthood would go through a similar trial via one means or another. This experience of death and resurrection is a common theme in initiations throughout history and geography. Whether or not the Ishtar myth illustrates a similar rite practiced in Mesopotamia is historically uncertain but is a popular idea in occult history.

In Greece, we have Theseus, Heracles, Odysseus, Orpheus, and Persephone to name a few; In Babylonia: Bel, Marduk, and Ishtar; Aeneas in Italy, Cuchulain in Ireland, Arthur, Gwydion, and Amathaon in Britain, and Ogier le Danois in Brittany - the list goes on. Most mythologies have a character capable of transcending death and returning from the 'underworld'.

IMO it probably all echos the Egyptian 'Ra' and his journey through the duat.