I think you have that backwards in the low rolling resistance thing. To have low resistance, you would need a harder rubber compound with higher tread wear rating, and in turn stiffer sidewalls to prevent flex to keep contact patch smaller.
It may seem counter-intuitive, but sidewall flex doesn't have much influence on contact patch area. In fact the upper half of the tire is the part that supports the vehicle with the sidewalls pulling against the carcass and belt structure, which in turn is under tension from inflation pressure.
The contact patch area supports the overall tire structure by inflation pressure keeping the belts stretched tight and pressed against the road. You can reduce contact patch area some by jacking up pressure, and that may reduce rolling resistance a bit but creates other problems. For the same pressure (and therefore same contact patch area), you have to do more work forcing hard rubber to deflect at the edges of the patch, generating more wasted heat, compared to soft rubber that just bends and bounces back. Sidewall flex is part of that story, soft tread and flexy belts help, too.
The tradeoff is that softer rubber doesn't last as long, and it may even be questionable if you save enough fuel to pay for the extra tires you wear out. But it makes the EPA numbers look a little better, so LRR tires are popular with makers, maybe not as useful for users. Though as a side note, they tend to be quieter than hard, long treadwear tires, for similar tread pattern.
That's my take on LRR. I did quite a bit of research before choosing Firestone Fuel Fighters for my Mazda. I don't think I would put them on a truck, though.