Am not against the idea of having a Director of Football, mind. More important is the relationship and ideas shared by the board and manager and as I said, we are seemingly moving in the right direction, especially with Cech on board.
Some of the names you mentioned there, work closely with the manager in regards to transfers. For example, Marotta now at Inter with Conte, again or Edwards at Liverpool (he certainly didn't buy players for Klopp to manage).
Of course no one would turn down the obvious talents to work with and not many top managers out there would just take a back seat and let others buy players for them. They want to have their own say as well.