Portista
Player Valuation: £225k
This Director of Football thing is interesting because in the States in all the major sports it is almost universally done this way. The Director of Football is called the General Manager, and the Manager is called a Manager in baseball and a Head Coach in everything else. With all the money involved with the PL, I never understood why transfers, players contracts, scouting etc were run by the same guy who was the touchline manager and ran training and tactics etc. Its seems like one guy doing two full time jobs, and the skill sets may not be the same for each. For instance, I rated Moyes much higher as a "General Manager" than as a "Head Coach".
Most continental football clubs also have a general manager/director of football (who can be a very hands-on club president). The autonomy and decision making amplitude of the head-coach may vary, but generally there's someone else sharing management responsibilities with him and directly handling most of the off-the-pitch stuff.
I also share your bemusement about the British way of doing things. How can the same guy have the time to do everything well? And, for example, who's running Everton right now? Who's talking to agents and assessing scouting reports and talking to other clubs and planning the pre-season and checking with the players and making decisions on the youth teams? We are out of a manager too but we've already purchased four players this off-season. If we were waiting for a new head-coach, we'd probably lose those bargains (at least I'm hopeful they were bargains).