This thread like most others on this forum, has migrated to a esoteric theoretical discussion entirely removed from the real world. The bottom line is quite simple. Since the average light aircraft needs about 50% more runway to takeoff than to land achieving the absolute minimum landing distance is rather pointless. In any case for the average PPL the problem is not adjusting the approach speed for weight of the aircraft..... it is setting the attitude and power setting to give a stabilized smooth flight path at a steady airspeed to the desired touchdown point in the first place
Finally despite what the POH says anybody who has any time flying a C172 knows that at very light weights (one person and half tanks) 55 kts works better for an approach speed.