There's no reason from a performance perspective why reduced or derated thrust cannot be used with Improved Climb V2 speeds.
It was originally a Boeing SUGGESTION that a Standard Flap setting be used for each aircraft type, with V2 min speeds, with which Reduced / Derated thrust was acceptable and preferred.
The SUGGESTION went on to say that if it was necessary to (A) Use a lesser than 'Standard' Flap setting, (B) Use Packs OFF, or (C) Use Improved Climb V2 speeds to extract the last Pound or Kilogram of Takeoff Weight, then no messing around chaps, use Full Thrust. (In other words, if you have to resort to a few trickeries to carry the weight, don't fiddle with the thrust).
Then along came the EFB and OPT (Onboard Performance Tool) which uses Improved Climb AND Reduced / Derated Thrust, and the SUGGESTION went out the window.
Along the way, many operators (including my own) adopted the SUGGESTION as a SOP.
History lesson over, back to the latest slanging match forum, hmmm, which one was that???
Regards,
Old Smokey