Quick answer (without too much thought)
1. V1 is based on runway performance, and therefore will change with reduced or flex TO thrust. (slower accel) Perf figures for the thrust setting should take account of this.
VR however is based on a/c weight and therefore will not change with thrust setting.
2. First flight of day - could be max thrust for thrust assurance check, or just too damn early to have brain engaged to think about the option!
3. Max thrust in noise sensitive areas will increase the climb angle and therefore the altitude, to reduce the noise footprint by the time you get to the measuring point.
Any other thoughts anyone?