I had the same thoughts as you. Here is what I found out with a set of older Hercules tires. (they came with the truck when purchased) When hitched with a WD, the rear truck tires were sagging a lot. The Hercules tires were perhaps not designed with a strong enough sidewall. No LT markings, but claimed a load rating of E. So, I increased the psi in all four tires to 42 from 33. The TT was set at 65psi, no changes there.
The ride was firm and felt planted. I was very comfortable with it all. What I found out over time was that the tires were overinflated and it predictably wore out the center of the tires within a short time.
Was ready for a new set anyway. The set I bought are BFG K02's. Load rating D. Current psi is at 35. Last time I towed, I made no changes to tire psi. The sidewalls are much stronger and did not appear to overly sag. Ride was excellent. My bad, I had too much weight in the front half of the TT.
The TT and I need to lose a little weight.
JMHO