Unless the manufacturer has a recommended pressure for the tire load, most folks run them at the highest pressure.
Just like your car, if you run at the highest pressure you get a rough ride and tend to wear the centers out of the tread. On a TT you do not notice the rough ride except to the increased jostling of the stuff inside, and it is unlikely that you will tow enough mile to notice significant center tread wear.
The only safety advantage is if the tire pressure drops a few lbs, chances are you will not be running above the tire's weight rating.
Usually the weak link in the chain is the axel rating. If your tires have a total load rated that is 200 lbs. over the axel limit. How much do you gain having them rated 300 or 400 lbs, over the axel rating?
You buy a premium tire for their reputation for quality. You have more confidence the tire will do what it is supposed to do, if you follow the tire maker's recommendations.
Good luck