The box won't get it wrong so
That is, sadly, not allways true. We had the case where the box (FMC) did it correctly initially and upon line up changed the target N1 values considerably, to a much lower value. Nothing happened as the P1 in question noticed it during the acceleration and manually overrided the autothrottles to max take off power, but if the take off would have been continued at the box computed values it would have ended in a high speed overrun. The box was replaced and found faulty lateron.
We used to have the tables for the reduced N1 computation on our checklist and had to use it to crosscheck the FMC on the first flight of a day, but that was discontinued after a few years of operation and the tables were removed.