I suppose a lighter fan would absorb less energy spooling up. Then less power would be required to reach a given RPM in a given time period, and perhaps the engine could be sufficiently responsive with fewer turbine stages.
Quite right. Steady-state, the driving torque to the fan
should be independent of the rotor weight (or more properly, its moment of inertial).
But during acceleration (such as GA) or deceleration, the lighter rotor will respond faster.