Anyone who says stage mix doesn't matter is obviously not singing any challenging vocals.
The better the band hears, the better the band plays. I do not like suffering while playing music.
Not only that, but if anyone videotapes you, their camera may pick up more stage mix than FOH. Why wouldn't you want to hear something similar to what the audience hears?
I get sound guys all the time "explaining" to me (as if I am a small, fairly unintelligent child,) "why" there should never be effects on vocals when they are in monitors.
I ask them if they would be explaining that to Aerosmith, if they were doing their sound.
Of course you want effects in your monitors. Effects mean you have to eq better, or you will get feedback. And these guys don't want to work that hard.
But effects also mean you know what your voice sounds like in the mains, and that means you temper your PERFORMANCE based on the ACTUAL SOUND, and not dry monitors. Does it make a difference? I'd swear to it.
As for instruments, I think the same thing is true, only to a lesser degree.
Put the guitar player in his sweet spot. Get his amp UP and pointing at his HEAD and EARS, not his KNEES, and he won't turn that amp up to ungodly levels.
Put a shield around the drummer. Not only does it make the stage more tolerable for everyone, but you don't have cymbals bleeding into vocal mics.
Our stage volume is such that we can talk to each other during songs, without screaming.
That comes in handy.
Bottom line: if you care about your performance, you should work to have a great stage mix. And don't let anyone bully you out of it, just because they don't feel the need.