In today's NFL, it's just as important that a coach be able to build a great overall coaching team, especially OC and DC, and have a great relationship/be on the same page as the GM on talent acquisition for systems run by the HC/OC/DC.
An offensive genius who sucks at other aspects of the leadership job probably won't have great success on the W/L unless they simply get lucky on their coordinator picks and the GM they inherit.
Let's look at two recent "offensive genius" coaches who have had success, and see if they had any other advantages that helped them in building a team and organization.
Kyle Shanahan - Yeah, I think being the son of two-time Super Bowl winning HC Mike Shanahan probably didn't hurt.
Sean McVay - Grandpa was an NFL coach AND GM. Also part of Mike Shanahan's coaching tree.
These guys both had highly successful leadership and managerial influences in their family trees and in their early coaching experiences, so they weren't overmatched by the HC job when their turn came.
Now consider Mike McCarthy. An uninspiring fired Green Bay retread to some, but he has the Cowboys performing at a high level as a legit contender, in large part due to bringing in DC Dan Quinn, and OC Brian Schottenheimer. McCarthy being the playcaller muddies the OC picture a bit, but in any case, retread old dog McCarthy has the Cowboys looking like they could go deep in the playoffs and even win a SB. He even has Dak playing at a much higher level.
Plenty of "what's hot right now" new HC's have fallen on their face because of leadership/culture/talent acquisition/bad coordinator hires. So let's hope, when the time comes, the Hawks don't pull a "Pete" and pursue whatever shiny object fascinates them in the moment, and hire the Percy Harvin or Jamal Adams (or Urban Meyer) of HC candidates. Let's hope they look deeper and find someone who has not just the Xs and Os guru tag, but also has the team leadership, culture, talent acquisition insight, and managerial skills to go with it.