Hard to believe somebody would say they do not help. Dodge trucks sway and yes you would like one. The most important thing is tire pressure. Trailer tires all get filled to the max pressure listed on the sidewall regardless of load and the vehicle should be checked for max pressure listed on the door sticker when ice cold. I swapped my sway bar bushings to polyurethane and run e rated tires so it's rock solid. Pulled thru a haboob two weeks ago that had all the trucks and RV's parked on the side of the road.
Re: "Trailer tires all get filled to the max pressure listed on the sidewall regardless of load and the vehicle should be checked for max pressure listed on the door sticker when ice cold."
Absolute nonsense.
Re: "Pulled thru a haboob two weeks ago that had all the trucks and RV's parked on the side of the road."
Your boat, unless it was a REALLY big trailer boat, has NOWHERE NEAR the big flat side area an RV or truck presents to a cross wind. If it did, you'd be parked right there next to the others - rear sway bar or not. There's something about seeing those up wind trailer tires coming up off the ground that will have you considering the idea of pulling over.
The rear sway bar controls body roll only - not traction or sidewall flex. Unless there is some new type of hitch I haven't seen yet, it's very difficult to imagine the trailer is able to transfer body roll it's experiencing through that coupler into the body of the truck. The OP states clearly his truck is equipped with a trailer tow package, and further has the stiffer springs generally associated with a 4x4 suspension. I doubt seriously a sway bar would hurt anything, but will it improve his trailering experience to any noticeable level? The factory didn't think so, and I'd have to agree. My opinion, FWIW.....