I agree with Darius that Rand is most unlikely to have given anywhere close to that much thought to the post TG world, when in COT he told Cadsuane that after TG the world would do what it wanted with the truce he meant to do with the Seanchan.

Rand hasn't picked Elayne to be the world's leader or anything close. He didn't want to act like a conqueror in his girlfriend's realm, that's why he wanted Elayne to return to power. He wanted her to rule in Cairhien to keep the nation behind him for TG.

He hasn't picked Egwene to rule the channellers either. There's not even a hint of that.

I'm pretty sure Rand won't be King of Illian after Merrilor.

I'm not even sure Elayne's multi-national rule will survive long. I wouldn't be surprised if before the end Elayne asks Galad to take the Sun Crown. Andor is about to need a full time ruler very soon.

Beside that, it's none of Rand's business. He's the light's champion, that's it, that's all. He's finally embracing that role and that role alone.