The idea that a higher "Load Range" means thicker or stronger tread or sidewall is not always supported by the facts.
Testing for Load Range includes a variety of tests. Sometimes there may be no difference in either the tread area or sidewall construction of two given tires and the only actual difference is the number of strands of wire in the bead bundle. This difference allows a higher "burst" pressure which is one of the tests a tire must pass.
Other tires may get a change in the steel in the tread area but no change in the sidewall. Each design is unique so no generalization can be made.
Thicker is also more likely to generate more heat at the same deflection and since heat the the major killer of tires, that can make thicker tires more prone to certain weakness. Again you can not make broad generalities that apply equally to all tires.
Now having said all the above I will say that I switched from LR-D to LR-E tires on my Class-C RV when new. The LR-D were capable of carrying the measured load at the placard inflation but I prefer to have a larger margin on my personal tires.
I run my passenger car tires at +10% over placard for better handling response and a minor bump in fuel economy.
I run my RV at +15% over the min inflation needed to carry the load. This puts me slightly above the inflation rating for LR-D. WHile I could probably back off and just go with the Max inflation on the tire sidewall of LR-D I wanted the ability to run higher pressure if I ever ended up carrying a lot more "stuff" on a long cross country trip as I did this Summer. I was able to increase the cold infl to 67/70 (above the 65 for LR-D) an keep my Safety Margin for load capacity.
My tires run cooler, I get slightly better MPG (My avg for 27,000 mi is 10.61 mpg with gas 6.0L engine in a small Class-C).