Okay so the situation is thus: Zag's mother Persephone left, and everyone is either pretending she never existed, and is hiding her identity from Demeter, who has absolutely dicked over the mortal realm in her grief. Hades is adamant that Zag never leave, even though he presumably is able to in a way he himself is not.

Now, it could be Hades is just a dick, and is cutting himself and everyone else off from Persephone out of hurt and spite, but it's plenty obviously that he genuinely believes Zag belongs in the underworld, and has even gone out of his way to give him a purpose there, even though Zag turned out to be trash at his job. Nyx too, isn't giving Zag any details as to why they kept the whole thing hush-hush, and we know damn well she cares abour Zag's well-being.

My theory is thus: firstly, Demeter would be infuriated if she found out Hades knew where her daughter was this whole time, and no-one wants her angry with them. Zag risks exposing the whole thing to her.

Secondly, Persephone left the whole underworld behind permanently, including Zag. The answer I think is the simplest, cruelest one available: she just doesn't want anything to do with him. And Hades, for all his assholishness, does give a damn about his son, and would prefer he not know he was effectively abandoned.

That's it. This game has done a great job of humanising the gods, and that's the most human reason I can think of.