Skin effect at 50Hz is about 9mm, so only makes a difference if each conductor is 18mm in diameter, that’s a lot of current capacity.
If you draw current at a higher-than-mains frequency when (say) playing an oboe through your speakers, that current will be passed back to the mains supply.
Unlike how an incandescent lightbulb draws power at a relatively constant rate (in time with the mains frequency), the PSU doesn't sit there and think 'I'll sip the power supply to recharge and hope there isn't a drum beat anytime soon', it tries to recharge its capacitors as quickly as it can (made worse by the rectifier bridge introducing a voltage drop, which increases the spikes of current drawn).
It's the change in current drawn by the music being played (in this example) that induces the skin effect, not the mains frequency (the impact of which, I agree, is negligible).