I've thought about this idea as well. Because character concepts are described by rolls, such as defender and controller, the class skills don't seem as critical for "niche protection."
Further, stats will allow certain classes to be the best at certain skills. A wizard can take athletics, but he's likely never to be as good as his strength heavy fighter buddy.
Now, the only issue I can see is that a lot of people will take perception, as it its the most common skill. Further, you may want to maintain the wizard having to take arcana, the rogue taking thievery etc just to maintain that consistency.