However, if both channels share the one power supply then a strong base transient on one channel is likely to deplete the PS caps, causing the power rail in the other channel to sag slightly. If the music playing in the other channel is predominantly treble music then you will hear distortion (I think this is is called Inter-Modulation distortion?).
Having one complete power supply including transformer for each channel prevents this happening. Having a separate mains cable, IEC socket, power switch and fuse is just "icing on the cake"!!
Regards,
Andy