Mozella, the reason is they fly a fixed Mach/Speed schedule irrespective of weight, they have no interest in the L/D.
"They" used to be "me" before I retired. I'm quite familiar with flying airliners having done so for 33 years. I've also done my fair share of sailplane racing. But fixed mach/speed procedures were not part of the discussion. At least I didn't think so. The post said, "............planning a min fuel burn descent without ATC interference."
It seemed to me that the situation involved stretching the glide using minimum power (since the head office, not to mention the passengers, get all upset if you shut all four down). That would be done the same way in a 747 as it would be in a sailplane; i.e. best glide ratio or best L/D. That's how you go the most distance for a given altitude, ignoring wind.
Of course, airliners have other pressing interests, cost being a big factor. That's why all speeds, climb, cruise, and decent, are faster than optimum from an aerodynamic standpoint. Each time the flight attendants got a raise we flew faster and each time the pilots took a pay cut, we flew slower as directed by the company bean counters.
Cost also explains why we didn't make decents at best L/D. It's simply too slow. But sometimes I flew slower even than that when, for example, I got instructions to hold at a fix for an extended period of time. In that case I immediately slowed to max endurance speed (minimum sink speed for glider pilots) and sauntered toward the holding fix at which time I accelerated a bit to holding speed. Efficient flying isn't hard, but you can't save fuel and/or time by being lazy which explains why some pilots raced toward the holding fix.
In our company, we didn't ever fly a fixed Mach/Speed schedule. Nearly every aspect of selecting cruse, climb, and decent speeds (and the associated power settings) took into consideration such things as the aforementioned cost, aircraft weight, wind, our schedule, leg length, other airlines published schedules, and even maintainance items which wore out based on time in service.
But I got the idea the theoretical 747 example was free of such constraints as well as ATC restrictions, but I could have misunderstood what was being said. That's why I asked.