Hades doesn't appear in the original Homer's Illiad or Odyssey. In real life, the Greeks did not like calling the Cthonic gods in name, believing it would attract them. You wouldn't want to attract the god of the dead.
Notice I didn't say "God of Death." That's Thanotos' job. Back to the point at hand, in mythos, Hades is always portrayed as incredibly busy. He probably wouldn't care about the squabble Athena, Aphrodite and Hera were having over that Eris chucked at Peleus and Thetis's wedding. Nor would he care about the resulting Trojan war. Nor would he care about Odysseus. Or any of the other Greek champions of the Trojan War. Hades is just a very busy man who just wants to manage the souls of the dead that pass through his domain, and get pegged by his very hot wife Persephone.