I am not a tire, oil, nor fuel expert--but TTBOMK:
1) The tire's maximum listed pressure is for max loading of the tire, not the truck.
2) The sticker is the proper tire pressure to support the maximum weight of the truck for that combination.
Changing tires of different sizes, weights, loads, etc. changes nearly all of the factory PSI formulas. There is some hard math behind it and other forums go into it in great detail.
As a general rule to be applied at your own risk, adding a few PSI above stock recommendation may offer better handling, especially where heavier tongue weights are concerned due to tire "squish".
Also, if you ran at full max load nearly all of the time (such as an overlander and we are talking 1500-1700 pounds of gear an passengers), you could see a benefit in LT (heavier load/duty) tires at the cost of some ride if emptied.
**This can be especially true if you are loaded heavy and air-down when off-roading.
**Airing down for off-roading is still bad for tire life overall, and heat buildup on road with too low pressure is terrible for tire carcass life (regardless of tread life). That is why the moment you get back on the road you really need to air up ASAP.
**Remember too, tires have a 'shelf life' due to exposure in years regardless of miles left on the tread, and this comes into play too.