No, it's not. The operative phrase in what you say is the "as possible". No one will disagree with the point that we all want as good an onstage mix as we can get, but most of us must compromise with the conditions we encounter at a gig. I have had (as I postulate most of us have) gigs from hell where we could not hear what we needed in order to play our best and our performance has suffered. No contest. No one wants that, but it happens and when it does, we tough it out. Sometimes we decide to never play that venue again.That's completely irrelevant. My point is it has to sound as good as possible TO ME. I need to hear myself and the balance of other instruments as best I can. THEN...it's up to the soundman to take THAT and make it sound as good as possible out front.
If I can't hear myself or I'm trying to manipulate a sound by "guessing" it's not going to sound good out front no matter what.
I don't think we disagree, fundamentally, but in difficult situations, the FOH mix trumps the monitor mix and the show must go on.