I mean, he's the eldest brother, right? So he's been in Kronos' belly the longest. When he finally gets free, Zeus has already licked the mortal plane like a big biscuit, and Poseidon dives into the sea, which he knows is the largest kingdom that isn't, you know, the underworld. So that leaves the biggest fricking can of worms in the universe for him to govern, and someone has to do it.
Maybe he hoped that since it was technically full of people, being the king of the underworld wouldn't suck so much, maybe he knew. In Tartarus, he has to punish the wicked, so basically it's a bunch of whining and world-class woe. The shades in the Elysian Fields have no memory, so I can't think holding a conversation with a bubble-headed, perpetually blissed-out bunny is going to be any kind of stimulating. And can you imagine the regular shades? All they have to talk about is the living, and their own spent lives--it'd be like listening to a balding, fat, former HS football hero who never gave up his letter jacket, 24-7. He goes from one bleak, isolated belly to another.
He and his brothers are gods, so culturally, this whole rapine thing is kinda their bag. But who the hell is going to go for the king of the dead, no matter what guise he wears? Zeus is bouncing around as swans and showers of gold, dropping demi-god offspring left and right in front of Hera's nose. Poseidon's off making horses and giants, surrounded by nymphs and fucking with sailors for laughs.
What does Hades want? One girl in all the universe. One beautiful, warm, living thing. And he still doesn't get to have all of her, because he gets the one MIL in all the universe who can strip the earth of life completely.
Dude.