I have a 2011 F-150 4x4 with the E-boost engine. I tow a 6200 lbs across the scales TT. I have not had any problems with the 6 speed transmission towing or not towing.
I tow with the tow haul because it delays the shifting. I also find the tow haul setting handy in the hills and mountains without the TT as it uses more engine braking.
I have towed over 25,000 miles in the last three years, I have found the OEM "P" rated tires adequate for towing and the driving around town. The towing did seem to take its toll, I had to replace the tires at 50,000 miles and the OEM shocks at 60,000 miles.
I have no doubt one can make bigger, stronger, tougher modifications to their vehicle but it's still an F-150.