When channels share a power supply you are robbing Peter to pay Paul.
That's not always true my amps power supply is bigger than most monoblocks combined.
It is always true. There is no such thing as a power supply that will not suffer from this. Some are just better at dealing with it than others.
The only way to prevent this in a stereo amplifier is by adopting a "dual mono" design - two monoblocks in one chassis