I always thought it was kinda funny how becoming the champion always went pretty much unnoticed among the npcs, yet in Pokemon Emerald you will constantly get calls from trainers commenting on your progress in the Battle Frontier.
Anyway, yeah, it'd be nice for some kind of significant changes after you beat the Elite 4, like people acknowledging you as the champion, maybe even have one rabid fan following you around and challenging you to battle every now and then. In other words maybe get a new rival after beating the Elite 4, who's goal is to beat you. Or maybe those npcs that walk around randomly in towns suddenly seem to be very shy around you and try to avoid you.
And maybe some sort of reaction from seeing you use a legendary pokemon in battle, or maybe recognition for saving the world. I mean I'm sure if you sent out a Groudon to attack some poor guy's Rattata he's going to go crying to his mommy and anyone who witnessed it will probably be going into therapy for a while, and it'd be plastered all over the news...
"This just in! The new Pokemon Champion has been reportedly seen using the legendary pokemon known as Groudon in battle!"
...Yeah I think I'm done here >.>