So can you crank in enough cyclic pitch to overcome this dissymmetry? Let's say you could. For a US rotation helicopter you need a bunch of right cyclic as you start going forward.
IFMU, the phase lag from dissymmetry of lift results in the blade reaching its peak of travel at the front of the disc, so you need forward cyclic to stop it, not right cyclic.
A rigid rotor would not have underslinging, so the coriolis effect would cause some extra stresses on the blades/grips/head, which a teetering head minimises.