Dig around Cliff's posts over the last 15 years, a lot of that randomness can be accounted for and is precisely why so many go to Fractal.
I've heard people gripe about modelers sounding too perfect and I never understood until recently. It's hard NOT to dial them into a 'perfect' state because the options are there. Some woofy low end on certain notes in an otherwise great sounding preset? Dial it out. A little fizz on the top that's just kinda gettin' to ya sometimes? Dial it out. Why not, the options are there and it's easy enough!
But these are the exact things about tube amps that could also fall under the 'randomness' umbrella. It's hard to unhear the idealized version of your tone in your head, but chances are, the idealized tone in your head is playing along with some other instruments that are going to have a big affect on how that tones ends up sounding, so if you START with the idealized version, by the time you had everything else in, you've now moved away from your idealized version and most certainly further away from the sound of a 'natural tube amp' on a recording.
There's definitely a lot of recordings as of late where I can tell they're using a modeler because the way it sounds. It's not that it's bad in any way, it's just the progression of guitar tones with the technology available at the time. Surely back in the 90's there were dudes saying "That's not a Marshall with an SD-1 in front, that either a Peavey or a Mesa"
I also suspect that's why you hear some people/bands having tracks re-amped through actual amps on albums, Periphery and Tosin Abasi are known for this, it's hard to dial presets back to being raw and 'unruly' like a tube amp after you've spent so much time making them perfect.
