RVD kept it in kayfabe "cause it spins", but also because if he threw it down, then there would be no WWE Champioship. I guess he liked havin' two belts, kept it as a prop, to rub it in Cena's face.
That's also why I think Edge keeps it, too. To fuck with Cena, because that's "his" (Cena's) Title. His whole gimmick these days is that He The Champ, The Champ Is Here, etc. and when he doesn't have it, he's chasing it. Seriously, if Cena wasn't in the WWE Title program, dude would have no gimmick at all.
See thats the thing I can see someone like RVD keeping it cause "it spins" and he thinks it's fun but, someone like Edge I figured would smash the belt into pieces to piss Cena off.