Where Does Gregg Williams Fit Into Saints History?

Saint Jack said
Or alternatively, how do you view Gregg Williams?
I ask this because the 15th anniversary of XLIV is creeping up and with that comes the accolades from that early ‘06-‘11 era.
Brees gets into the HOF and the Saints Ring of Honor with Payton following him at some point.
Various players getting inducted into the Saints HOF. Even some executives.
But what about Williams. Does he get excluded from any of this because of the events of the offseason of ‘12? Or does he get a welcome back.
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I felt like he was scape-goated for a while. Then I didn't like what he did as a coach other places and think he just kinda got lucky here. Had a lightning-in-a-bottle season, underwhelmed with the rams and a couple AFC teams.

I thought this part of his wiki was interesting though:

New York Jets​

On January 16, 2019, Williams was hired as the defensive coordinator for the New York Jets under new head coach Adam Gase.[44] While the Jets offense struggled, Williams led the Jets to seventh in the NFL in overall defense including second against the run.[45]

On December 7, 2020, Williams was fired from the Jets following a 31–28 loss to the Las Vegas Raiders. The firing came after Williams called a controversial zero blitz on a Hail Mary play as an attempt to sack Derek Carr. However, Carr found Henry Ruggs open, beating corner Lamar Jackson for a game-winning touchdown with five seconds left, thus dropping the Jets to 0–12.[46][47]
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