The issue is not sidewall flexibility. Forces that allow tires to turn corners are much more complex than simple bending of a tire sidewall. The primary issue is the Cornering Coefficient that is developed by the tire as the path traveled differs from the direction of rotation.
You can find some background info HERE.
The actual issue you might want to think about is not simple side bending but twisting stiffness. Cornering forces are transmitted from the wheel through the tire sidewall by twisting, then to the belt package and finally the tread rubber. Each component has an inherent stiffness that tries to resist the turning forces.
The cornering force generates a shear force between the belts and the body. That is a relatively weak link. If the repeated forces exceed the strength of the rubber to resist tearing than you have a good chance of experiencing a belt/tread/body separation. Once this separation grows in size over many hundreds or even thousands of miles these components come apart. When this happens the tearing may be limited to just the layer of rubber between the tread and top belt or between the two belts or between the bottom belt and the body. This tearing can easily move to the rubber between the body cord and result in a breach of the air chamber. This leads to a rapid loss of air pressure which many incorrectly ascribe as the reason for the failure and not the result of the failure. Hence the "I had a Blowout" complaint. Yes the driver was surprised when he heard the loss of air but he often jumps to the wrong conclusion.
Increasing tire inflation, as I have often suggested, can alter the cornering forces and the sidewall stiffness and the 'slip angle". Finite Element modeling has identified the level of shear forces between various components and found that multi axle trailers can experience 24% greater shear forces that tires on a motorized vehicle.
offers additional information on Interply Shear.
You have it in your power to lower this shear force by:
Increasing tire inflation and by Increasing the Reserve load
with higher Load Index with the associated increase in inflation and by Increasing the tire size that will also increase potential max load capacity and result in increased Reserve load.
RE LT tires vs ST tires. IMO I think you are more likely to find the latest technology and best durability in tires made by the "Big Three" or as applied OE to current model Pick-ups.