Moridin has one massive asset: he wishes for himself something only Shai'tan can give him - the final death of his soul - and his best chance to get that is to ensure Shai'tan's final victory.

Moridin is the only Chosen truly motivated to do anything and everything to make Shai'tan win, and who make any personal agenda a distant second to that. Moridin is Nae'blis because he's the only Chosen who puts so little value in the position itself and understands it must be him because all the others are too self-serving and ambitious. Moridin doesn't care for the title or to boss the Chosen around, all he cares about is using them like pawns on a board moving toward Shai'tan's victory. He sees the Chosen, even himself, exactly like Shai'tan does see them: expandable means to an end. An end he wishes for too. That he understands all this and still wants to serve makes him invaluable to Shai'tan.

Demandred can't be trusted. He's a man who lets his feelings get in the way (his hatred for LTT) and he was a traitor, a backstabber. You can never trust very far a traitor. He didn't join the Shadow out of conviction, he joined it almost at the last minute because he was convinced the Shadow would win, and siding with the Shadow gave him an opportunity to bring down LTT in the field. You can't trust a man like this as Nae'blis and Shai'tan would be a fool to trust him too far. All Demandred can be trusted for is to wage war against Rand and his forces, devise military strategies and implement them. He's perfect for that. But at the first whiff that Shai'tan intends an end to everything, Demandred would abandon the Shadow - not for the Light for sure, but he would make sure to accomplish his goal of killing Rand before Shai'tan wins, diverting any Shadow resources he needs. Whatever happens, Demandred won't want to die before Rand does.

Demandred can never be Nae'blis, because Demandred's real priority is Rand al'Thor, not Shai'tan.

Only Moridin can be trusted to handle the global strategy as Shai'tan devises it, because he's the only one Shai'tan can tell openly about the global strategy and the real endgame. He's insane by human standards (even those of the Forsaken) but I think Shai'tan rather sees in him the only human who thinks more or less the way he does.

Mind you, the position of Nae'blis is a sham, and Moridin knows it and doesn't care one bit. There never was any real intention to have a regent of the DO on earth, after his victory. Shai'tan named Moridin Nae'blis only because his position as leader of the Forsaken was shacky after their awakening, and Shai'tan tired of them putting more efforts toppling one another than serving his goals.

At this point, there's too few Chosen left to name another Nae'blis anyway. There would be no point. The real orders come straight from Shai'tan/SH anyway. Moridin is more or less a front, and seems satisfied with the sham. The Chosen blame all the weirdness of Shai'tan's orders on Moridin's insanity, and meanwhile they remain unaware that the real "madness" is Shai'tan's.