I think the Sporting Director / Director of Football role is one that has different job description at different clubs. I also think it has evolved over recent years to something more aligned to supporting the manager and coaches, rather than setting out how the team should play and / or identifying targets.
A good example is Edwards at Liverpool. He was there before Klopp arrived but Klopp has defined the way the team have played. Edwards has worked with Klopp on identifying players and he has experts working for him such as scouts and data analysts doing lots of background work. He is then involved in getting the deal done. What manager wouldnt want that sort of team to work with? Hopefully a conversation can be had that convinces any manager doubting a Sporting Director that it doesnt mean their control is eroded.