Tow haul mode, changes the shift strategy, and raises the line pressure, to reduce the chance of slippage, causing heat build up. It is recomended always when towing or hauling.
Unlike the old days, when the tranny's had OD, the old version simply turned off the OD. The new design, doesnt have the OD but another gear, and The tow haul mode switch, will change the perameters of the shift requirements. Holding gears longer, downshifting earlier, not unlocking the converter, on decents, down long hills reducing brake fade.
I would also add Ford doesnt put an exact weight, on when it is advised to be used, because then there are variables. This way, if you are towing or hauling, use it. Keeping it simple
I drive a motorhome so in my opinion I am alway carrying a load and I use the tow/haul all of the time.