I do agree that thick cases take energy to bend and rebound, but they also take more energy to overcome cracks, rocks, and other debris. When a rider runs over a small stick if the tire has high pressure the tire will bend less (saves energy) but the rider has is pushed up vertically to get over the stick which requires energy. The energy comes from forward motion and is expelled as vertical energy which slows the rider. If the tire has less pressure it will absorb most of the sticks vertical movement. But this comes as the expense of the loss of rolling resistance from less pressure. If you take two tires, one supple and one stiff, and use ride them at the same tire pressure, the supple tire will absorb more of the vertical movement. The stiffer tire will not flex as much because it is not supple which requires more forward energy to be used to overcome the stick.
That being said I'm speaking purely about which pressures would be faster, without caring about ride quality. If you're goal is least energy vs ride quality I'd guess, assuming you're not a clyde, that you're tires are over inflated if you're running them 130-140 psi.
I understand that and agree - except on many roads 130-140 is not there. Speaking of road riding...Any pressure that causes your tyres to bounce and lose contact with the pavement very often, is too high. It is a calculation/risk that must be made for a race. Any pressure that will reduce friction beyond what is needed to ride, is too high.
Other than those two, for minimal resistance - higher pressure is better. I think we are agreeing based on what you posted.
My reasons are both personal and the experts I've asked and video of experts (I posted video above of the Garmin TDF team mechanic). They ride in the 120ish-130ish range. Francois (FMB and the TT tyres for Sky) says high - the TT bikes with his tyres are run 140-150. The Vittoria site calculator puts many riders over near 130psi.
I would like to see public data that indicates what pressures are too high. I have only seen data to indicate for racing and the TDF - 130 is likely not too high (which was my one line post).