Filter capacitors in unregulated linear power supplies

The VA rating of the secondary windings of a transformer is defined as V_rated*I_rated*PF. The power factor is less than one in linear power supplies and the larger the capacitance of filter capacitors the lower the PF value. So, it's not a good idea to reduce ripple as much as possible with filter capacitors as this has the effect of reducing available power. Ofcourse, amplifier transformers are overdriven all the time but overdriving produces waveform distortion, which is probably a contributing factor to the rising slope of the distortion curve when it approaches rated power.

Am I missing something?