Threads about tow/haul are funny.
Most mechanics I talk to say t/h will help the transmission to last longer / run cooler, some say don't worry about it.
A friend of mine drives his truck in t/h ALL the time, towing or not, to "save the transmission".
I use it whenever I am towing.
With my 2008 F250, the t/h does NOT "lockout" overdrive, just waits to shift into it until you are on a flat road for awhile. The downshifting to help in slowing sometimes kicks in more than I think is necessary, but it works great.
I have slowly come to agree with those who say to not overthink it... let the engine computer figure out the best gear. If you really don't like what the computer is doing, you can do it manually.
Edited to add: keep in mind, I am driving mostly in New England. We have hills (basically no flat spots! lol), but I really haven't driven in real mountains much.