These aren't my words at the bottom, but some guy on the PRS forum. I tend to agree with his point however, that the amplification matters more than the guitar, and hey that's how this post started (and in a very poetic manner!):
Then somewhere around September, the amplifier picks up. That pretty much carries you down to the last two weeks of the year. Well, on one of those two weeks nobody does anything, so you’ve got five days left. And in those five days, everything else anybody wants to argue about, be it pickups, paint, wood, cables, capacitors, anything—that all falls into those five days. It’s an insignificant part of the total experience.”
From the PRS Forum:
"What complicates things is that one can dial in a very wide variety of tones on any decent guitar. Add an amp, and you can morph those tones into other tones. Throw in a few pedals, and you're further away from the sound of the guitar.
Throw on a different cab and speaker, now mic it with a 421 instead of a 57, and it's going to be even more different.
My point is that there are endless tones one guitar is capable of. Who on Earth can always identify how that tone was originally generated?
But the question isn't whether you can identify a particular guitar later. The question is whether you can dial in a tone you like in the first place.
For the most part, that requires using a guitar whose sound you like to start with.
You mention that you often go direct from the guitar with no amp or effects (and presumably no modeler), which, to my way of thinking is and has always been the single most generic and mediocre-sounding way to record guitar of all time (and yes I know it was big in R&B and disco, cool, fine, I don't care). Amps create an important piece of the guitar tone puzzle, (more than half IMHO) and their exaggeration of tones and frequencies coming from the guitar help define and establish the guitar's tone. I don't know why, but it's true. Even modelers do this.
My theory is that it's because guitar amps aren't linear devices, they are highly colored, their frequency response is crazy-uneven, and guitar speakers are even worse, in a good way.
I had a very linear bass amp, a Mesa 400+ with full-range speakers and a tweeter. A higher fidelity rig works great for bass, but try plugging your guitar into a rig like this -- it sounds absolutely horrible! Much like going direct!
Electric guitars need to interact with a guitar amp for some reason. Something good happens." Allen Scheman