The filter capacitor charges during a small part of the full-wave rectified 120 Hz cycle. At 60Hz, the half cycle time is 8.333ms. The charging current pulse lasts ~2msec. For about 6ms, the filter capacitor has to hold up the voltage.
The filter capacitor(s) discharge at a rate dependent on the instantaneous music power. During a quiet passage, the voltage sags very little. During a loud music passage, the voltage sag could be substantial, depending on the source impedance of the power transformer, the capacitance of the filter capacitor(s), if left and right channels have independent power supplies, the peak power being delivered to the speakers, etc. The voltage sag could be reduced by making the filter capacitor(s) bigger, and by having independent power supplies for right and left channels. You dont want a loud passage in one channel effecting the other channel; hence it is better to have independent power supplies.
PSRR is a measure of how good the amplifier is at not feeding the filter capacitor voltage fluctuations through to the speaker. If you have amplifier(s) with good PSRR, you can have a crappy power powe rsupply. If your amplifiers have poor PSRR, then you need well regulated supplies.