Hi Lu
You may be moving off topic by bringing up blade symmetry; but for the fun of it ......
Rotor blades and their airfoils appear to be a very complex subject. A subject that entails art, theory, experimentation, computer modeling and a Ouija board. Some airfoils will pitch down when the angle of attack is increased, others will pitch up. Some blades are now produced which combine these opposing features in the same blade. Composite construction has allowed the helicopter blade to have varying attributes along its span.
Even carbon and Kevlar fibers may be replaced by silk. Just this week it was made public that man-made silk has finally been produced. It is 10x the strength of steel.
Your point about the lack of torsional stiffness in rotor blades is another sound argument for rotor rigidity. Mind you, all this torsional, in-plane and out-of-plane stiffness is going to play hell with the feathering bearings.