Why diesel trucks?

It's all about the mountains for me. My experiences towing through the Rockies and Sierra Nevada mountains has been lackluster at best with a gasoline engine. For me, a diesel is well worth the expense and reduced payload for these situations.

You buy a diesel for the performance. THe diesel makes it power at lower RPM's.
In the end the diesel is providing more low end torque/power creating a more relaxed experience. The engine is not spinning as fast or revving as loud vs. a gasser. The transmission is not shifting or searching for the right gear.
The diesel is simply more capable when at the extremes.
If your only towing a few times a year on flat ground a gasser will be OK.
However if you tow regularly especially in hilly or mountainous terrain you will want a diesel.
The big three will all have a larger gas motor in 2020 which may change the equation going forward

With the new gasoline engines coming from Ford, Ram and GM there is no real need to have a diesel engine just to haul a TC. If you plan on towing a large trailer then a diesel may be the better choice.

I bought an older low mileaged mint DRW to haul my beast around for less than 1/3rd of what a new one costs. Not many if any older Ford DRW gassers around, so diesel it was. Pretty much a diesel only game with Ford F350 DRW’s in any year really. I have a company rig I make my living in, hard to justify a new deticated camper/boat hauler with a few beer runs sprinkled in for around 4k miles a year. BTW, my work telco rig is a gas powered V10 2017 F450 DRW. I get 6-7 mpg. Glad I don’t pay that gas bill! My Diesel with the camper on it gets double that and the power is nice to have.

For just a TC there is no good reason to get a diesel, as you have noted it actually reduced the mathematical payload of the truck.
I also use my dually for other truck purposes like towing equipment trailers loaded with excavators around so as a dual purpose vehicle diesel makes sense.
One reason many people have a TC is they can tow large trailers behind them. I did that with my boat behind the TC also. With my fully loaded truck, camper, and boat I was around 18,000 pounds.
Also, a diesel dually is much easier to find on a dealer's lot and much easier to sell than a gas model.
If you are only hauling the TC or towing small trailers and you intend to keep the truck a long time I would get a gas engine.

A DRW truck hauling camper means it's that much easier to drag a big heavy trailer behind you if not now then someday.

With a SRW, diesel is probably overkill but many prefer it anyway.

Without towing, your camper weight is within the range of what a V6 could tow.

For me, it’s a diesel to be able to more easily pull the mtns and I’m assured no issues towing anything that I ever might want at a reasonable speed.