Just a musing, but on the large fan engines, I felt that the packs had less to do with total max thrust, than with the associated EGT margin.
Thus if you have lots of EGT margin (based on sea level hot day takeoff) than the engine limits the max thrust by burner pressure and rotor speed. If you open bleeds to power packs than your EGT goes up and may then become limiting to the engine before it achieves its maximum thrust capability.
Any other tech comments for or against this point?