The issue with a DOF for me is I don't really know our identity at the moment. Simply taking Edwin (or their actual DOF Overmars) wouldn't guarantee success. Difference is more subtle but important:
With Ajax, the philosophy is ingrained in the club and so former players coming through from various eras will have similar ideas of how the game should be played (a generalisation of course but I think overall very true) so if Overmars quit and another former player came in, the type of player they recruit and general way the club operate wouldn't necessarily change. That's not to dismiss Overmars' work in any way but Ajax are a collective. Edwin is the CEO so he's more involved in strategies and the commercial side as I understand it, however he comes from the same system and understands the club. They have a clear idea of what they want and how they want to do it.
Another example is Barcelona, since Rijkaard they have brought in a number of former players who continued their success and play (with some differences) a similar style of possession based football. I believe the one manager they who wasn't a former player (Martino) was the least successful. When we watch Barcelona the world expects to see a certain brand of football.
With us, SAF was the identity and in many ways was an embodiment of the club. How many times did people speak about him dragging players across the line, not playing well but winning and also building different teams with different styles. The guy was a genius but the issue now is what do United want to be, how do we want to play and how do we think we can differentiate ourselves. Generally people attribute direct, counter attacking football with wingers with SAF but we never had, at least in my mind, a set philosophy and we seem very uncertain about our future. Since SAF retired we have hired Moyes, LVG, Mou and Solskjaer - you couldn't find a weirder list of managerial appointments and stylistic clashes and that's the reason we have such a random assortment of 'big' players who don't really suit us.