Why do I need a W/D or sway control

A good sway control system is good insurance.
You may not think you need sway control but someday you may have someone cut you off really bad or have to make a very radical maneuver to miss a deer, a moose or worse a pedestrian and then you may find out why you may need sway control.

You probably don't. I wouldn't spring for one if the truck doesn't sag and you have no problems with sway.

Whoever told you you needed one was either trying to sell one or has too little TV for their rig. Just my humble opinion.

I do not have either TV or trailer like yours. I tow a 21 foot, 5000 GW TT behind a diesel SUV rated to tow 6,000 lbs without a WD or sway control. Works fine. No sway, tows straight as an arrow.

F-350 Dually? or
the amount of sway is controlled by the tires.
the dually should be good to go

You don’t. Unless you do. But you don’t. Lol.
WDHs have become the ultimate travel trailer owner security blanket. Plain and simple.
Yes some combinations NEED a wdh to reduce effective tongue weight. Like if I used my half ton to pull out toy hauler.
And some (likely few) need sway control to assist with poorly weight distributed trailers or marginally short tow vehicles for the length of the trailer.
Since you don’t fall into either of those categories, you don’t need the RVers binky.

Proof of above theory, count how many “other” bumper pull trailers you see with wdhs. All of them. Boats, cargo trailers, flat deck tag trailers. And compare trailer size to vehicles towing. The number will be zero or almost zero.
More proof. Pintle hitches. Why are the heaviest trailers towable by light duty trucks not even made with a hitch that can use a wdh?

Wdhs are the product of a good invention turned into a marketing scheme by RV dealers which has now, with the internet, propagated into some sort of brainwashing by RVers.

Btw, I have a wdh I’ll sell you. Came with my last camper. I’ll knock $50 off if I don’t have to clean the dust off of it!! Lol.

A Weight Distribution Hitch may be required in order to meet the load ratings of for the receiver attached to the tow vehicle's frame.

Look at the receiver and note the load ratings on the labels. Usually two ratings, one without WDH and one With. Without is often far lower than With.

As for sway control, proper loading and tire pressures (on both trailer AND Tow Vehicle are often the best methods of sway control. A Friction type sway control is all I use on my 6300# trailer and sometimes I even leave it off with no sway issues.