The reason why I ask is that, as much as I love some of the Cataclysm content ("Yes, my horse IS made of stars"), I got into the game only recently, and I'd like to experience the story from the beginning instead of being thrust into the middle of it. It wouldn't be too hard to implement, either. There isn't just one huge world that everybody plays on; there are dozens of realms, so it would make perfect sense to have both pre-Shattering and post-Shattering realms. Players without Cat would be restricted to the pre-Shattering realms, whereas players with Cat could choose between the two, though they'd experience the same restrictions on the pre-Shattering realms as everyone else (like being capped at level 80). This would give players a much greater incentive to buy Cat; as things currently stand, the only reason to buy Cat is for the Worgen and Goblin races, because you're getting everything else for free. Also, because Bliz allows players to transfer their characters from one realm to another, they could transfer characters from pre- to post-Shattering realms, but not vice versa, just like you could convert Diablo II Classic characters to LoD characters but not vice versa.
Also, there are plenty of players who genuinely hate the post-Shattering content, and they're contributing to an explosive growth in the popularity of illegal private servers.