It is more important with high speed digital circuits to have good return paths for the signals, as the return path tries to follow as closely as possible the signal path.
So copper pour is used to make power planes, one layer a ground plane, the other the supply plane.
It is not a good idea to flood the signal layers, as the greater area tends to radiate noise and crosstalk.
This is in fact, quite a complex subject and not one that can be answered in a few short lines.