There were several flop games in the Payton era. Surely you remember the turmoil of the 2014-16 seasons, yes? Junior Galette, Brandon Browner, Keenan Lewis, Jairus Byrd, et al?
Dennis Allen, if he isn't the solution, will not merely be demoted, and I only have all of modern NFL history to support that claim. If the team decides it's time to move on - which, it should be noted, is not how the Payton era ended; he stepped down - they will give the next head coach the opportunity to bring in all of his own people. The upper management didn't make Sean Payton retain any of the very fired Jim Haslett's assistants, they cleaned house. I could not find a 21st century example of a team saying "this coach couldn't hack it here as a head coach, but we'll keep him and just have him coordinate a side of the ball." I don't know where Saints fans are getting this idea that this will be the team to retain but demote a head coach, but it's both a bit disconcerting and counter to all common knowledge of the sport to say the least. George Seifert told the 49ers to pound sand when they tried to hire Steve Mariucci to replace him, and they were a losing franchise back in salary cap purgatory two seasons later before firing Mariucci for turning it back around and wanting credit for doing his job well. It took them a decade and four coaching changes to recover. I don't want the Saints doing sloppy things just because it's doing something.