The dictionary defines a system as " a set of connected things or parts forming a complex whole." The electric guitar - amp combination certainly meets this definition.
As a studio owner, dealing with mic preamps, mixers, etc., where gain staging is important to prevent (or when desired, cause) audio artifacts, I would also say that gain staging is an important issue that also applies to the guitar-amp system.
Rane has a useful definition on its website. It defines gain as, "the amount of amplification (voltage, current or power) of an audio signal." As a PRS guitar has very useful volume pots, and amps these days often have both gain and master volume controls, there are lots of opportunities to shape the signal. Yet I often see even very superb players fail to take advantage of the multiple gain stages in their guitar equipment, and in so doing, lose the ability to color and control their signal in significant ways.
If all a player does is turn the guitar controls all the way up, and then turn the gain up on the amp, set the controls, and leave everything in one place, not only are the sonic options decreased, there's literally nowhere to go when the tune or the solo calls for a little more emotion or a different sound. So people have to stomp on a pedal to get there, and while that certainly can work, a world of color options go missing. Not only that, but the capability built into a really good amp to respond to subtle gain changes from the guitar is completely wasted.
It's often said that music is not only notes, but emotion. In my experience, emotion is a subtle thing, and when you see great players constantly adjusting their guitars while playing, you're seeing them use the controls to help express the most emotion from a tune.
To have only one clean choice and one dirty choice out of your system is like having a singer who can hit the right notes, but only can whisper or shout, nothing in between. Boring!
A tube responds to the signal coming from the guitar, and most amps' "gain" controls are preamp gain controls (most amps' Master volumes are for the power amp section). That is, they control how much signal is going to hit that preamp tube. And the tube responds to the gain from that signal by either passing it cleanly, or distorting. The beauty of tubes is that the distortion sounds interesting because it throws off certain harmonics and attenuates other harmonics as it distorts. If enough signal hits the tube, it goes into clipping. If the tube clips enough, the sine wave entering the tube becomes a square wave as the peaks of the signal are "clipped" off. A fuzz box is an item that sounds like it does because it generates square waves by operation of its transistors driven into clipping.
To get why the waves can be important musically, it's because they sound different. On a synth, for example, one generates a clarinet sound with square waves, a piano with sine waves, and a violin with sawtooth waves. Then the harmonics are filtered to create the coloration that lets you identify the particular instrument. A single note from a very highly overdriven amp sounds more like a saxophone than an acoustic guitar's single note because you're generating square waves by heavily clipping the signal and creating them via the overdriven tubes. And a sax is very much like a clarinet in how it generates sound; it's a square wave oscillator.
Thing is, these waves are easily shaped, and the tubes respond very smoothly to the nuances of gain in a great amp!
The HX/DA, for example, is a perfect amp for me because it responds so gradually and smoothly to gain changes. IMHO, the corresponding ability to control the output of the guitar into the amp in a really good way via pickups and output knob is part of the coolness of PRS guitars.
If you set your amp up to sound a certain way with the guitar's volume and tone controls set lower than their maximum output (I set mine up to get a desirable sound with the volume as low as 2 or 3), then you can control your gain, and your tone color, with the guitar volume, and with a good amp you can get an immense amount of color out of the amp.
In fact, I think it's a bit of a waste to not use that capability to the fullest.
It's not just a matter of "cleaning up" the signal by rolling off the volume either. It's that the tubes will be able to generate a tremendous variety of tone coloration because of the nature of how the circuits go into distortion and clipping to generate a variety of harmonic content. If you aren't gain staging your guitar system to take advantage of all this stuff, you're really missing something cool!
With as many pickup, amp, switching, and other choices as there are in the world, it's not possible to say where to set what, as every piece of gear is different. But what I am suggesting is that players acclimate their ears to appreciate the desirability of achieving these tone colors, and learn how to get them in their rig.
I do understand that there is a temptation to go for the brightest pickup sound with everything full-up, but with proper gain staging you can do that anyway. What I'd submit is that it's the in-between stuff that can make playing a more interesting and rewarding experience, especially for the audience. And to me, what separates the men from the boys, and the women from the girls, in an amp is the ability to sound good and respond to lots of different settings.