Absolutely untrue. There are some really brilliant coaches, but for the most part, professional sport coaches are not hired for intelligence traits.
If that were true, few former players would ever become coaches.
The biggest factors in coaching are organizational skills, motivational skills, and teaching skills. Most schemes these guys follow are legacy schemes concocted by other coaches..
there rarely is more than one or two coaches in any sport at one given time with any high end Strategic abilities.
I dont think they are stupid, by any means.. but i wouldnt call them smart.. they are average to slightly above average. You get one or two really smart ones who can actually do the other coaching things once or twice a decade at best...
They should have a separate college class or developmental program for Coaching.. much like the military has a separate program for officers... then you could get really smart, creative, and strategically adept person who understands how to team build and motivate...
I think Tomlin has been a top 5 or 10 head coach every year... but Id bet his IQ is between average or maybe a few points above that... his big picture vision ability is meh.. he mostly plagiarizes tactics.
Coaching in the NFL isn't great... but it isn't meant to be... homogenized tactics lead to parity.. and that's great for entertainment..