I feel that the DoF is currently just another staff member. I believe that, in real life, they are much more (if they exist at all in the club). In some clubs, they are a central figure. I would like to see this more well explored in FM.
The club could have an imposed structure on who decides about transfers - the manager or the DoF. This should be part of the contract negotiation with new clubs and could be a feature of the game that could be turned off for FM players that want always to control everything.
If the DoF is in charge of buying and selling players, two things should happen:
The media, club and supports should not complain with us about new signings or sells;
Before a transfer window, there should be a talk with the DoF indicating which type of players do we need to get in the team (position and ability) and which should be released.
There should be a relationship between the DoF and the manager. These dynamics are also very important within the club.
The club should be in charge of hiring this DoF and their policy DoF-manager could change during a save (if this option is turned on).