I had the opportunity to follow a small TT down the road. It was a rental and was hooked to a large enough TV. This thing was swaying back and forth like mad. I backed off and watched for a while and noticed that as long as he was going below a certain speed it was fine. As he sped up it started wagging again.
That impressed me to get a hitch with built in SC when we purchased our 21ft. hybrid. I was towing with a 4Runner and it was plenty strong enough and even the tongue weight was fine. I wanted some weight distributing properties so I went with an Equalizer that does both.
If a trailer is properly set up and the weight is distributed as it should be and if your TV is strong enough, you probably could get by without either and just put it on the ball. Too any "ifs" in there for me. Having a huge 1 ton might help you avoid the need for WD but I really don't think it will stop a trailer from swaying when it happens. Better safe than sorry is my idea.