The generalization on DoF and football structure is just misleading.
Just like with tactics, style of play, management style... even with similar approach and principles, there is still variation in the outcome. Nobody is the same. So the structure, and role of DoF, the vision at different clubs can be different.
We, United fans more often than not like to compare ourselves to Liverpool. Let be honest, we would prefer a manager, the type like Klopp, mostly for the longevity reason beside the football style. And it looks like our structure is being closer modeled after theirs than other clubs.
Liverpool model however is more manager reliant than others. Of course, head coach/manager is vital to any structures. IMO the manager/ head coach has more important role. Their work are demonstrated in the limelight for all to analyze. Football is played on the pitch after all. Better manager would mask deffiency of the structure in the background. SAF and other great traditional manager back in the day are the proof of that. Klopp to a lesser extend (he prefers focusing on coaching and having a DOF) still a bigger influence than their structure in their success. And don't believe there is another Klopp at the moment. If Klopp ever leaves Liverpool any time soon while their structure stays the same, they would pretty much be back to their pre Klopp state, which is not unlike our current state: having talented squad and the manager can be good but the team doesn't look to pull in same direction; the feeling of something missing always there; a change require a longer rebuild.
So among the DoF, Michael Edwards IMO, is not all that. He and Liverpool benefit from having Klopp. There are DoFs out there that look like they're less reliant on a manager, and their work have discernible effect on their teams: Paul Mitchell, Marotta, Campos... And some DOFs' role is the boss of manager/head coach. So nothing to see here re: Liverpool and Michael Edwards. So even if we scale down our expectation from looking for a SAF to looking for a Klopp, IMO we're still out of luck. There simply no other like that currently out there. We need to modify the structure and DOF's role further, so we can self sustain at high level during the transition. By high level I don't mean challenging for CL, and the league every season. Still similar objective like top 4:regular CL football, but aiming to win smaller cups also. Even when we're out of the CL, we have to aim to win the competitions we're favorite for. The byproduct would be shorter amount of time needed for rebuild, as players are conditioned to work toward the goal of winning. Once the correct manager comes, he wouldn't need to teach them the basic, as well as need to get new half a squad of experienced winner to set the standard, and few seasons for everything to fall into place. It's easier to restructure the background settings than finding a perfect manager, in case the manager need more room to flex.
Structure, DoF, manager, CEO... all the fancy concepts all boiled down to balance and decision making, just like the football on the pitch. Yes. Many of us are well aware of the big names we have been recruiting to our recruitment set up. However, just as with football, how to make a functional, high performing out of it is another task itself. It still feels off with decision making at this club. From signings that unaligned to a certain vision/style, signings that can' be utilized/ no pathway to the team, to weird contract renewal of players and staffs, inability to move players. Right now, IMO Ole is given the power similar to Klopp, which our equivalent to DoF is not his boss, so the decision making is still someone else upstair responsibility and those are still failing at his job. It maybe better structured than it used to be, but right now it is still not proactive enough regarding succession plan. Who extended Ole and Mike Phelan contract? Were they happy with their progress, and unaware of the performance all this time (prior to this season), so that they don't have a plan for this situation? All they, football people now have a role to input for next manager appointment, but why they were not heard before (Ole and Mike Phelan)? They are not heard now, but would their input appreciated in the final decision?