A few years ago, we had a Flight Engineer who incessently pushed up the throttles very rapidly, and one of our Captains nearly ended up in the weeds....twice.
When this turkey flew with me, I reminded him quite distinctly just who the engines (and their handling) belonged to, and he left the company shortly thereafter.
To everyones complete satisfaction.
Now, I personally prefer to set (approximately) the correct takeoff thrust, then ask the Flight Engineer to...
trim throttles.
Everyone seems satisfied, and...it is the company standard procedure.
Imagine that.