So far my “P” type Wrangler tires have worked just fine. We put 8000 towing miles on the RV this summer. I have had hard stops, swerves, wind buffets and foul weather without issue.
We spent time camping in the Rockies and the flat land of the Everglades and even snowshoeing in Indiana. It was about as diverse a selection of road conditions as you are likely to get.
I suppose if I had issues with sway or bounce or some other TT performance, I would be taking a serious look at alternate tires. But my ½ ton pulls my 6000 lb. TT just fine. I just as soon not mess things up.