PSRR stands for power supply rejection ratio. It's a measure of how well a circuit shrugs off power supply variations. However, a single figure can be a bit misleading. A circuit could have a very good PSRR at 50Hz but a much less impressive PSRR at 1kHz or 20kHz.
People have been doing things about it for a long time. The obvious solution is to use a regulated power supply but it has to be very big and expensive to compete with a simple unregulated supply.
An alternative approach which I have used myself is to split the "output" part of the power amp from the "input" part. The output needs a beefy supply, so leave it with a simple unregulated supply. The input part doesn't draw anywhere near as much current so it's feasible to use a regulated supply for that.
Some designers say that there's no need for any regulation at all because a well designed power amp (with good PSRR) doesn't need it.