I see that in at east 2 posts above there is the contention that if the TV is big / heavy enough sway is not a concern. This is not correct.
Sway is resonance that is induced on the trailer that has nothing to do with the TV.
That said, if the TV is large enough, the instability is reduced vs if the TV is small. That is it. There comes a point beyond which the instability will affect the TV regardless of size. Even if the TV is steady as a rock, I am sure none of us will drive anywhere behind a trailer that is wagging side to side even if the truck is going down the road apparently dead straight.
In the final analysis, there is all likelihood that the owner will select a trailer to match the capability of the truck, so any sway induced in the trailer will affect the rig as a whole. No one will get an F450 and pull a 1200# popup.
The question is how to minimize the sway. The place to start is to balance the loading of the trailer (12% on the tongue) and then add a properly sized anti sway system.
OP - yes, you need a WD system pulling that 21' trailer, okay? Skim off some of the common points from many of the foregoing posts and you will have your answer as to why.