"Solve that one and you are on to something."
Yes, it's called a helicopter rotor system!
Ignoring the other factors for a moment, I'm not sure why you desire this propellor like rigidity? If you had a rotor blade that was perfectly horizontal while not rotating, it would be massively over-engineered compared to the strength it actually needs to function when rotating, this in turn would lead to the whole head and gearbox structure being over-engineered to cope, and for what purpose?
A propellor is too short and light to derive the required stiffness from rotation; a rrotor blade is not.