Right... and that is how life will always be.It's only "identical" with identical speakers, and certainly not everywhere in the venue. This is the crux of the dilemma.
If it isn't the same everywhere in the venue, then that is on the venue's acoustic, sound system, and engineers... not on us.
But having the same identical source going into your amp and into the mains and monitors, and having your amp not alter that tone (so it becomes FRFR which hopefully the mains and monitors strive to get close to also).. is as good as it can get. The engineering for the mains and the various speakers throughout a venue, the artificially added time delays in the speakers that are setup further from the stage so the time matches with that of the mains... all of that is way way outside of what we, as musicians, have control over.
The live mains sound engineers will alter your tone, intentionally, and there's not much we can do about it since it's way bast our hands as musicians, other than complain to the engineers, I guess.
IMHO

