..........props are more flexible, which means that when the engine speeds up, the prop twists and the angle of the airfoil tends to flatten out a bit.
Actually, that's not always what happens.
A prop blade is an airfoiled wing. Some airfoil shapes do have pitching moments. Those moments may be strong or not. Some are close to the max thickness of the airfoil, some are not. Some props are just like wings and have different airfoils at their root than at the tips. Some have cambered airfoils at the roots with more symmetrical ones at the tips. Symmetrical airfoils don't create pitching moments.
Sometimes the load on the prop will actually cause it to try to increase it's AOA. And that's not necessarily the aerodynamic load. Just because a prop is flexible doesn't mean it flexs toward flat. Nor does it mean it flattens. It could increase AOA.
It's risky to apply simple ideas to complex things.
Most prop manufacturers understand all the complexities of the situation and capabilities of their production methods. And know that what they want to sell when they brand a prop 10x6 is a prop that pulls 6 inches worth. And they use whatever their production methods are to create a 10x6 that pulls 6 inches worth of pitch. Their 10x6 may not be actually be a pure 6" pitch because they expect it to flatten (or twist more).
We may have an engine with the power to get 6" worth of pull or we might not. Our engine may need the flexible prop to help it get 6" worth or it might need the stiff one. And truth is, the engine might run better and wind up putting out more power with less pitch.... and get less with the stiff one.... or not..... or whatever....... it ain't sound bite simple