Here is the 737 FCTM extract:
Engine Failure During a Reduced Thrust (ATM) Takeoff
Since the reduced thrust (ATM) takeoff must still comply with all regulatory takeoff performance requirements, it is not necessary to increase thrust beyond the reduced level on the operating engine in the event of an engine failure. However, if more thrust is needed during an ATM takeoff, thrust on the operating engine may be increased to full rated takeoff thrust by manually advancing the thrust lever. This is because the takeoff speeds consider VMCG and VMCA at the full rated takeoff thrust.
Increasing thrust on the operating engine to full rated takeoff thrust provides additional performance margin. This additional performance margin is not a requirement for the reduced thrust takeoff and its use is at the discretion of the flight crew
Messing around with thrust is an additional task in a demanding and critical
situation and yet adding thrust would increase your rate of terrain separation.
My view is that one should dispense with rigid solutions and simply remain situationally aware and assess the risks, remain flexible and attempt to go with the least risk option by balancing sensible precautions with workload according to the conditions.
Sometimes you just have to agree to disagree. Personally, I endeavour not to be railroaded by examiners, instructors and Captains (or any other more experience pilot). I don't know what your experience level is, but I found that the confidence required to politely push back on advice that lacks merit, especially during a recurrent sim, takes time to develop.