tinyrice
How very eloquent.
For somebody with an apparent occupation such as yours I am, suprised that you did not know that jet aircraft are often weight limited due to length of runway, low ambient air pressure, ambient temperature or lack of decent wind component. Using the APU to supply bleed air will increase the amount of power available from the engines and hence increase the max take off weight from a given runway with one or all the adverse factors mentioned above. The calculations take into account losing an engine at the most critical point enabling the aircraft to still get airborne and clear obstacles.