Just to give my take on it, compression and "moving the fader" are two different tools in the arsenal and both have their place since
the effects are also different.
"Moving the fader" is, if we're honest, mixing. I use that to
control the balance among multiple channels to make things sound good. If I'm honest, I'll sometimes also use it to reduce the overall level of multiple
tracks so that, when mixed together, I still have adequate headroom at the master fader (though this becomes less necessary/relevant with 32 bit floating point mixing). Moving the fader doesn't change the overall sound of an individual channel; it just changes the balance between that channel and others.
Compression, on the other hand, makes changes (sometimes subtle, sometimes blatant) in the way your source channel sounds. We've been talking like the peaks and quiet bits can be viewed (or listened to) in isolation. They can't. If I've miked, say,
an acoustic guitar there will be the loudish fundamentals but, going on at the same time, lots of harmonics that give the instrument it's full rich sound. These are at different levels but occur at the same time on the same track. If I apply compression, it brings the fundamentals and harmonics closer together in level terms thereby changing the character of the sound.
This is not so say the compression is evil or bad. It's not and, in both multitrack mixing or
live sound environments it's often necessary. As soon as you add other sounds (be they other tracks in a recording
session or just air conditioning, moving lights and crackling
sweet packets in a live setting) you start to lose any sounds below a certain level. Compression that narrows the dynamic range coupled with some make up gain makes sure the subtleties can still be heard. The trick is to apply the compression with sensitivity and being aware of the effect you're having on the overall sound.
A final comment is that, for me at least, fader moves controlled by ear, not by watching meters, are absolutely essential to the mixing process. Yeah, in my time in broadcast sound I've used ducking amps and the like but they're no substitute for the human input manual mixing gives. Similarly, using compression to control dynamic range can also be essential, especially in the noisy
world we now inhabit.
Although I enjoy them from time to time, discussion of voltage swings and RMS levels are good for background understanding but they don't tell you how something actually sounds.