indeed. saturdays are quite enjoyable and also for live spectators. a meaningful replacement session would be required to justify their paid attendance.
a hybrid idea of a sprint race (15 laps for the to try to get to the front) run in reverse championship order in lieu of the quali session could work.
but then you would have to change the PU allotment rules, relax parc ferme and work hours to allow for repairs, more tires...all of which would cost more money etc etc...i guess F1 is just to complicated to allow for these sorts of changes!