I actually have XL rated tires on an F150.. It's a 13, but it's a MaxTow with 7700 GVWR... It has the OEM 20' wheels with 275/55/20 tires on it. Also the OEM size.
The XL rated tires I have is 50 psi max and #2833 max load per tire...
Since the rear axle rating is only #4050 I'd say the tires far exceed the axle rating so why get LT E tires???
I think all the LT E tire recommendations came from those that don't have a late model F150, or ever towed with one... ;)
Anyway, do whatever you want to do.. Get some heavy E rated tires and pump 'em up to 80 psi and be happy.
I did what I did and I'm happy as it's what works for me.
Good luck!
Mitch