I remember that when I was a Type/ Instrument Rating Examiner on the B757/767 (I'm retired now) the 2-engine go-around was frequently performed untidily in the sim, so much so that I included this procedure in my 'How To Do Well In The Sim' paper. It's disappointing to learn that crews are still getting themselves into trouble flying this manoeuvre.
I was also a T/IRE on the B737 and that was also my observation.
I think a lot of this is sheer lack of practice. How often do pilots do an all engines Go Around (either on line or in the Sim)?
In this situation given the all engines performance, the low relative level off altitudes are a potential threat and IMHO should be briefed for.
That's why there are two pilots in the cockpit, both of whom should be adequately qualified, experienced and not fatigued.
Discorde, of course! But taking over in this situation requires a lot of advocacy.