Here's one data point from out here in the real world. Over the last two days I have towed one of my horse trailers a little over 500 miles. Half the miles empty, half with Mister horse in it. Same roads.
This trailer has a 7500 GVWR. Weighs just under 4000 pounds empty ( on the CAT scale ), so we'll call it 5000 or so with the quarter horse in it. Load range E tires were 78 psi cold yesterday morning.
The trailer pulls extremely well, empty or with the horse in it.
Point being, there are some folks who would say if you run too high of a load rated tire, it may not "tow correctly" ( bounce or whatever they may want to toss into the argument ). I can tell you at least with this trailer, this truck, blue ox swaypro hitch, my driving on various roads from standing still to 65 mph..... it tows correctly.
I like my load range E tires. They are black, and go round and round. That's cool.
Over and out.