I still don't see how this is Rand's concern in any way.

It's not that Rand doesn't care - certainly not after his epiphany - but it's not part of what he's meant to do.

One of your affirmations was that Rand has chosen Egwene to lead the channellers in his place/after him. That's completely twisting things: Rand didn't lead the channellers in the first place, and he's not in any way chosen Egwene. The female channellers, the Pattern if you prefer, have chosen Egwene, post-epiphany Rand has stopped opposing stuff like this, that's all. Egwene's there, it's Egwene he'll work with. The Asha'man prefer to be lead by Logain than him, he won't oppose that either.

Rand isn't the Wheel of Time, though for a long time he acted as if he could control it. He's stopped doing that now. The Pattern will see to itself again once Rand has done what he must do as Champion. His job isn't to shape the fourth Age, it's to make sure the world doesn't end with the third.