IMO, ideally, you don't want a GM-controlled org chart. You want a Head Coach-controlled org chart. That's how most winning teams operate. Coaches like Kyle Shanahan, Mike Tomlin, Andy Reid, & John Harbaugh may work with GMs, but in all of those cases, it's the coach who really runs the team. The GM serves the coach's vision, even if he hired him.
That's what we had with Payton & Loomis. And it seems to some extent that's the way it's set up now under DA. It's just that it's not working.
There is a severe lack of true CEO-level, "Head Coaches." Most of these guys are just coordinators who call plays and leave the other side of the ball to someone else.
All that to say, I think the Saints system is fine. It's the same system under which we had so much success. We just need to find one of those rare coaches who has a clear vision and can build an organization that is aligned with that vision.