Yes but the clubs above that are SUCCESSFUL have other senior people overseeing the football-side of the organisation. I'm not advocating getting rid of Woodward altogether, I'm advocating hiring experts to run the footballing-side of the business. Ideally we would have;
Director of Football - Ultimately responsible for implementing a 'vision'/ethos, ensuring a strategy/philosophy is implemented and practised across the club, from the way the U9s play football to the way we assess potential transfer targets to the coaches we hire etc....
Head of Performance Analysis - Ultimately responsible for assisting the manager in providing Data-driven assessment of our own performances and opposition performance
Head of Recruitment - Ultimately responsible for implementing Data-driven approach to Scouting and recruitment. Oversees scouting network, which can be reduced in number as they no longer have to trek around the globe watching games, instead create a small team of analytical experts who learn about players from statistics.
Head Coach - Responsible for ensuring philosophy is implemented on the pitch, that the players act as a cohesive unit, overseeing coaching/training and tactical approach to football matches
Now, as far as I can tell, and we would be guessing here because none of us actually DO know, we don't have anything like this structure. I would assume that Gary Neville has some insight into our structure (former player, connected to the club, at least two of his best mates/business partners have been employed by the club very recently) and Gary tells us it's a 'shambles'.
Head of performance analysis has always been part of the managers team at United. Moyes had his own, Mourinho his own for example. I am sure Solskjaer has someone as well.
Head of scouting operations (as its called in United) is Steve Brown.
When it comes to DoF/Head Coach that is continental semantics. Guardiola is still called manager at City even if they have a strong "DoF" in Txiki and Guardiola is basically coaching the team.
United is traditionally the club in England - at least now post Wenger - where the power over the footballing side lies with the manager the most. When Gill and Ferguson quit that suddenly; there were no plans in place to develop the club in a different way. And why should there have been. You dont fix whats not broken. That was not on Woodward, who was promoted to replace Gill CEO for CEO, while Moyes was drafted in to replace Sir Alex one scottish manager for another. Accountant for accountant (to use your terminology). It was on Gill and Sir Alex who thought and still thinks that this is the way a football club should be run. All power to the manager. This is a very important fact to have in mind when one considers what happened later.
The CEO role did not change though and still has not today and will not for the future. Or actually it has with the listing on the SE which gave Woodward way more corporate redtape to deal with than Gill had when United still was a private company.
Then Moyes came in and royally screwed everything up. What he did do was to identify that we had a non-existent scouting network and were trailing the other clubs in the league, even his old Everton in this regard.
The LVG "era" was at least a plan for the future; grooming Giggs for three years, etc. It also led to the club starting to realise that it had been falling behind in the youth setup as well. LvG did not work out either as we all know.
When we then chose to appoint Mourinho the new scouting network was built. I think we went from like 5 to 58 scouts in two years. Its also when the talk of appointing a DoF started, which is natural because important functions of that work is to oversee both youth and scouting.
Mourinho had no interest working with a DoF though. My guess is that the club wanted him so much that they agreed to not pursue that appointment until his tenure was over. Problem was that he had no interest of using the clubs own scouting network either. In many ways Mourinho always wanted the United job because of the fact that so much power has lied with the manager himself, recruitment included.
IMO the push for a more progressive organisation has if anything come from Woodward. The man is not a masoschist. He knows that appointing a DoF does not change his role at the club. It does move responsibilities and more important accountability first and foremost from the manager, but also from the head of scouting and head of youth setup to the DoF. Nothing else.
Because that is were the footballing decisions have been taken at our club ever since Sir Alex and Gill left: by the manager. Of course within the financial framework set by the club, but that is another matter. The positive effect for Woodward is that a DoF essentially creates another firewall between him and what happens on the pitch/the fans and people will be screaming DoF out instead of Woodward out. I think he kinda looks forward to that.
We have advisory board members for strategic footballing decisions; Gill, Sir Alex and Charlton for example. You just need to read one of the great man´s books to understand what his opinion is on a more progressive organisation that devalues the role of the manager. Their commitment to the ways of old and the appointment of Mourinho are the two major things that have maybe hindered the progress of the club´s organisation IMO.
Finally, I am for a DoF. But it will not have the allpowerful effect on the club that some believe. That will take time to settle as well. We need to be patient and realise that the club actually is moving in the right direction. If slowly so be it. And that has actually been set in motion when Woodward took over. He gets way too much crap here - your original post included - for involving himself in "footballing matters" when he does exactly what Gill did.