A 454 powered C20 can tow a hell of a lot more than 7,000. My C30 is rated for 9,000 when the actual weight of the truck full of fuel is subtracted from the GCWR. I'd say that a 454 truck has to be able to pull at least 10,000 lbs, of course depending on the gear ratio.
I have had no issues with even the biggest of trailers with my C30 except the lack of power because mine has a 350. It will pull damn near anything safely with D rated tires, a good brake controller, a class 4 reciever hitch, and 15k lb. Reese 5th wheel hitch, and huge brakes. The only thing I've got to be careful of is to not overload the rear axle or the single tires on the back. Not having a dually is about that truck's only weak link.