The lighter and softer the suspension on your TV, the more you might need a WD hitch. Passenger tires as found on SUVs are also not very stiff and can contribute to sway.
Modern 1500 pickups have soft suspension and will sag farther than a 2500 under load. That's OK. Trucks are designed to work well with different loads. One of the best things you can do is install a set of premium rear shocks that are velocity sensitive and preferably, adjustable. These will dampen the vertical movement and keep the tires planted. Then make sure you have a high quality brake controller that is set up right.
A heavy duty truck does not need a WD hitch for an Oliver. My Oliver tows better than any trailer I've had and it never plays any tricks on me. Never.
I bought my Oliver when it was one year old and it came with an Anderson WD hitch. The first thing I did was look at how it attached to the frame of the Oliver and the stresses it created. I decided based on that that it would not be used. Plus the hassle of hooking it up just right every time. I frequently unhook at the campsite and drive off on the TV.
I just can't see those clamp on frame brackets, clamped to an aluminum frame and relying on friction and a set screw, doing much weight distributing. Sway control, yes, but not much weight distributing. Be sure to frequently check those clamps.
My TV is a Ram 3500 SRW and I keep forgetting Ollie is back there while towing.
The other thing is greasing the ball. Absolutely grease the ball, especially when using a WD hitch. My Ollie has a tongue weight of 425 pounds vertical load. Using the WD hitch adds another fore and aft load of hundreds of pounds. Then braking and accelerating add more fore and aft loads. All of that transferred directly from the ball to the coupler. The ball swivels with the coupler on an Anderson hitch, but when going through dips, into driveways or over uneven surfaces there is movement and wear at the ball. Balls and couplers never match precisely and there is galling with no lube.
I find it interesting that Anderson recommends turning off your sway control if you use their hitch and it feels unstable. Really? The idea of the Anderson hitch was to add sway stability. Why defeat one system to accommodate the other? Better to try it without the hitch first.