How much you can tow with a C or an A gasser will depend on the size of the motorhome. More weight in the motorhome, less weight you can tow.
Ford gives the E-450 chassis a GCWR of 22,000 pounds, maximum tow of 10,000 pounds. If the motorhome, loaded, is no more than 12,000 pounds, the 10,000 is there for towing, unless the RV manufacturer had reason to downgrade the maximum tow. Many install a 5000 pound hitch at the factory.
The base F-53 chassis used on a gassers today is GCWR 26,000 pounds. Put a 16,000 pound motorhome on that, the chassis can handle another 10,000. Put a 22,000 pound motorhome on that, you have only 4000 left. Again, the RV manufacturer may have had reason to limit the tow to something less than Ford's ratings, and I don't know of any coming from the factory with a 10,000 pound hitch.
You have to watch the ratings on diesel pushers as well. Most capable of a 10,000 pound tow will be above the 33,000 pound GVWR class. Pusher chassis in the 26,000 to 31,000 GVWR class might have less GCWR margin for towing, so it depends on which chassis was used for the build and how heavily it gets loaded.
I see motorhomes pulling Yukons, Suburbans, full-size vans, even two-car enclosed trailers, but they are almost always top-level diesel pushers in the 40,000 to 50,000 pound class which will have a chassis with 400 to 600 horsepower and 60,000 to 70,000 pound combined weight rating.
Having to spend an extra $100,000 to move up to a motorhome that can tow your big SUV leaves a lot of room to buy a smaller towed vehicle. I have a 2500 pound car I bought for towing behind my C (which can tow at least 5000) and has a side benefit of getting 30 mpg running around town (close to 40 highway, but I like something bigger for long trips).