If PM doesnt push Thrust Levers all the way to TOGA and they are put into CLimb after the V1 cut, you won't get MCT until they are (briefly) put into and out of TOGA position. ( don't ask me how I know this...)
Hey,
Did not really get all the process you are describing, but anyway, if you get an engine failure during takeoff, you are either in MAN TOGA or MAN FLX. If you are in MAN FLX and you don't select TOGA thrust (you don't have to from perf calculations), when you will need to select THR MCT you will need to move it out of its detent because FLX and MCT have the same lever detent. That is the only reason. In single engine moving the lever out of FLX/MCT and back again is like saying I don't want FLX takeoff thrust anymore but MCT thrust. As soon as you are back, you get THR MCT (provided you are in OP CLB) and A/THR white.
cheers.