Excellent, I've always thought NSNO has a bit more enlightened fans than other forums. What I've seen in them there have been much more people rejecting the idea out of hand because it doesn't work at City or whoever.
Toffee_scot put down the reasons why a DoF is a good idea well. It's also worth realising that a good manager doesn't necessarily make a good DoF any more than the reverse is true. They require somewhat different skills. That's why I would scan through clubs using this model and see which are doing a good job from this perspective. Clubs that are punching above their weight over a period of time including more than one manager, who have a good transfer policy and a good youth setup with a clear vision for the club.
The last part is something Everton needs as well. What sort of image should the club have in ten years time? There are plenty of clubs that are known for a style. Tactics come and go but underlying principles can stay. We were known as School of Science but what does it actually mean? Should the club define it set it as the goal to aspire to? At least to me it looks like our greatest teams (mid-80s and period from 1963 to 1970) had a few things in common: skill, determination, grit and mentality. They played good football but they were also tough and had people who hated loosing. IMO, that would not be a bad place to start defining the requirements for a team.
DoF's job would be to see that player recruitment would be on the right track. There would not be too many players who don't fit into the chosen style. This way each manager (who would also be chosen to fit the club) would only need small adjustment rather than whole-sale changes making the transition much smoother and quicker.