The Greeks were more preoccupied with, where these ousted gods resided. That is: The fallen son's of God could go where humans were, but humans could not go where they were. According to Greek mythology, Tartarus was an imposed condition for bad gods--not bad humans. (page 10)
GETTING KILLED BY TARTARUS didn’t seem like much of an honor. As Annabeth stared up at his dark whirlpool face, she decided she’d rather die in some less memorable way—maybe falling down the stairs, or going peacefully in her sleep at age eighty, after a nice quiet life with Percy. Yes, that sounded good.
Yeah, you bet Romani.' Percy bared his forearm and showed them the brand he'd got at Camp Jupiter- the SPQR mark, with the trident of Neptune. 'You mix Greek and Roman, and you know what you get? You get BAM!' He stomped his foot, and the empousai scrambled back. One fell off the boulder where she'd been perched.