I count trucks pulling 5th-wheel travel trailers (don't count horse trailers) on my trips. More than 80% of the trucks are SRW. Hard to believe that 4 out of 5 people are wrong in their choice of a SRW truck for towing.
Everyone I know that tows a 5th wheel using a SRW truck. Once the trailer is at a campsite they would much rather be driving a SRW truck around the area.
DRW helps with a very heavy load in the bed of the truck as 4 tires support more weight than 2 tires, but DRW provides no similar advantage for most towing situations. The drivetrain has to work harder with DRW and that affects the towing capacity as you have just learned. Where I have usually seen a DRW truck used is with 2WD trucks where the extra tires at the rear help with traction on dirt and gravel surfaces.