Mass is not linearly proportional to length, because a longer rotor needs to be a lot heavier to be structurally sound. A uniform rod is not a good analog for a rotor blade. It's not a far fetched idea to think that the mass is cubically or at least quadratically proportional to the length of the rotor.

Unfortunately I can't remember the source where I saw the 5th power figure.

In addition, the aerodynamics of a rotor don't scale up linearly either.

Your assumption is way too simple. Mass increases with the cube of the scale, while cross section area increases with the square of the scale. The cross section will need to increase to cope with the extra mass, and that in turn will increase the mass itself, and this mass is specifically the rotating mass.