Do you see what I see?
Always use a monitor so that you can see what the camera sees without making your DoP move. On rare occasions, a monitor is contraindicated, but those are very rare occasions. You always want to know what the camera’s seeing.
I was on a set a while back where the Director had no monitor and the DoP and he constantly locked horns about what was in the viewfinder. Afterward, in editing, the Director found out the DoP had been moving the camera each time after the Director had approved the shot. That’s some crappy rapport, for sure!
It’s a valid point that the Director and DoP should trust each other, but this does not means the Director shouldn’t be watching the monitor anyway.
“Trust” is a tricky thing.
My favorite DoP is a fine shooter and I’ve worked with him for more than a decade on lots of projects, but I still insist on a monitor (and he also insists I look at the monitor instead of through the camera: “Go to your monitor, Edward!” he often says), and still make suggestions based on what I see.
And, likewise, he makes suggestions to me as well.
It works very nicely.