Saints planned to interview Mike McCarthy; McCarthy didn’t garner enough interest from Saints and will take a year off

Hedon James said
you left out probably the biggest epic failure of all....Steve Spurrier.

But Dick Vermeil (UCLA), Bill Walsh (Stanford), Jimmy Johnson (Miami), and Jon Robinson (USC) might tell you something different. Even Barry Switzer (Oklahoma) may want to have some words. A Lombardi is a Lombardi, no matter how it was obtained, IMO.
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Out of the list you gave, Vermiel and Walsh already had significant NFL experience.
They were NFL guys taking a pit stop at college.
JJ is the one outlier in terms of a CFB coach turning pro.