Your volume level is actually the single most important aspect of your entire mixdown. Before equalization, before compression, before stereo imaging and harmonic excitement and multiband processing and all that crazy hoodoo voodoo stuff people slap on their chain to make it sound "professional", your mixdown relies upon the level of the different signals.
The reason people rarely mess with volume faders after setting them is because volume determines depth - the louder a signal, the closer it is perceived. the quieter a signal, the further away or "down in the mix" it is perceived. So in the traditional mixing mindset, you want to achieve the best sound possible with the volume faders alone before even touching the pan pots or any post processing. From there you can pan the sounds to give each signal more space in the stereo field, then start post processing with EQ and compression and whatnot
only as is needed by the sound and within the context of the track.
EQ and compression
can change the overall amount of level of the tracks they're placed on, but that is why they have output gain controls - to trim or boost as necessary to return you to the volume of the signal before it was processed. So if you're doing some surgical EQ and cutting out like 2.5-3 dB of information, instead of boosting the whole track that much you can just add a couple of dB of makeup gain within the EQ.
I don't get the logic. What difference does it make whether you're increasing or reducing volume?
Think about it. I have this vocal I wanna post process. I'm gonna be compressing it, putting saturation on it, sending it through a reverb, and in the end it's all gonna get squashed through my mastering chain. If I start adding frequencies that were not originally present, what do you think might happen when it starts going through all these effects?
Of course, there are no hard and fast rules - if it sounds better to boost instead of cut, do it! As long as you are aware of what is happening and
want that to happen, there's no problem.