The title of this thread is even more interesting when applied to the sporting/technical director role across the sport, I think. What are they, exactly? Walking Rolodexes, data wizards, charismatic salespeople, football visionaries? In truth, I feel like a large part of the role is actually more like a bagman for managers - managers have to feel as if the entire structure is there to support them, that the team is being molded in their image, their every need is met (within reason), and that they are also kept honest and focused on coaching (Wenger lost this specific support and desperately needed it). All the while, the TD is simultaneously establishing a strong foundation that won't collapse when that manager gets sacked/leaves. In that sense, I think you don't really know how well a TD is doing until the manager changes over.
At Arsenal, all of this is complicated by our penchant for visionary managers, who might further obscure the background work of the TD by taking on many of those romantic roles. So maybe Edu is really more of an enabler, and I'm not sure there's anything much wrong with that as long as we are set up to continue an upward trajectory when Arteta leaves. In a weird way, that also means that a TD has to give a manager enough rope to hang themselves with, otherwise you couldn't tell who was doing a good job or not. Then you have the further complication of Edu potentially leaving before Arteta, which would basically mean we never get much insight into his actual job performance. Might be the best move for his career, actually, if Arteta wins something big with Arsenal and Edu uses that moment to leverage a move to another big club to keep up the mystique.