Studio monitors, or aka near-field monitors need to be flat and have lots of headroom.
The rest of your thoughts are simply discussion points.
In the end, it doesn't need to be 'specific to the Axe-FX' in a studio setting at all. The key is hearing what you are getting accurately, with as little color as possible. And your room acoustics come into play on this too, as important or even more-so than your actual monitors. The entire system is indeed a system that must function hand-in-hand.
That part can't be stressed strongly enough unfortunately.
The only thing that I'd like to add to this is that something that I've learned (correct me if I'm wrong), but when shopping for monitors and then coming home and installing them I discovered that what sounded 'best' to me and what was more accurate were two different things.
As an example, people seem to love to use Bose stuff (I never understood the buzz) but they do have their application at the end user level, but if you tried to use them to do accurate mixes chances are that your settings are going to be very colored (of course, we know that).
But going away from the extreme analogy, there are still plenty of monitors that sounded
more musical to me than what I ended up buying (sounded warmer, more bass, a little wider), but that was all coloration from the monitor. As you know you need to get something that is as flat as possible and that doesn't always sound the most pleasing so keep that in mind when A/B'ing them. Your ears are going to gravitate towards what we enjoy listening to and have been conditioned to think of as good quality speakers, you want something that is critical, linear across the audible spectrum and that you can hear imperfections in the audio.
So the most accurate monitors may actually be the ones that sound the worst depending on the source of your audio. :razz
I remember when I got my monitors and new audio interface home, hooked them up and started questioning myself immediately. Every MP3 I had sounded bad. My old speakers and consumer soundcard sounded great compared to these. It was the first time I ever heard all the errors that all those 'tone snobs' had been talking about for years. Nothing was wrong with my monitors, on the contrary I finally had a system that was going to show me all the warts so that I could catch them before it went to the final product.
What I discovered though was that listening to songs that I grew up with I was hearing things in the songs that I never even knew were there. Every instrument had it's own space and I remember thinking "I didn't know they used a tamborine on that song" or hearing a cowbell buried in the mix somewhere.