In a band setting, I think it works better for a multi-instrumentalist to be able to shape his/her own sound using a little Mackie type mixer onstage, and whatever other effects. But mixing a band...it can be done, but ultimately you need some ears at the back of the hall, (a pair of ears who can communicate the needed info to the onstage board, which is inevitably distracting...)

It may be distracting to performers (we try to be subtle), but we're just trying to get the best sound to the audience. People switch or trade instruments, and all of a sudden the balance needs to be shifted again, which may or may not be evident from the stage. As for the monitor mix, it's there for the performers convenience. I have no idea why a sound person would change it on the fly unless specifically requested to do so by the performer.

Willie-O