The New Orleans Saints never had to choose between Dan Campbell and Dennis Allen because of the timing of Sean Payton's year long hiatus, but per Terron Armstead, the players would have chosen Campbell.
Payton stepped away from the game after the 2021 season, a year after Campbell joined the Detroit Lions. 2021 was from the first time Payton was rumored to leave. There was a rumor that Payton could go back to the Dallas Cowboys in 2019. If this was the summer of 2019, it's hard to imagine Payton leaving right after the No-Call. That could be why it didn't happen.
There wasn't any hesitation around what the players thought the Saints should do. Make Campbell the head coach. He was the assistant head coach for years at that point, and it always felt like he was next in line. The players certainly agreed. Armstead detailed how the players were perfectly fine with Payton leaving and Campbell taking over.
Being forced into picking Dennis Allen instead of Dan Campbell set the Saints back years
Personally, I've always wondered what would have happened if there was a choice to be had between Campbell and Allen. It was pretty clear the Saints were going to go with an in house route, and it's hard to be too frustrated about that logic with all the success of the Payton era. It didn't work out in hindsight, but rolling with Campbell could have yielded different results.
Watching the ascension of the Lions since Campbell took over has been impressive to see, and Armstead's story further hints that it could have been the Saints. It didn't start off smooth, but he was able to right the ship, and they haven't looked back since.
Campbell is known for being gutsy and there may be no better show of that than trading Matthew Stafford for Jared Goff immediately. Stafford was clearly the superior player, but he needed a change of scenery. It's less about the players and more about what the decision represented.
It's difficult to imagine Campbell settling for Derek Carr. It's not just because Allen being Carr's former head coach made this a natural fit that wouldn't have existed with Campbell. Campbell also would have been more aggressive in his pursuit of Drew Brees' replacement. Playing it safe simply isn't in his nature, and Carr was a very "safe" decision.
Landing on Campbell completely changes the recent trajectory. From mentality to coaching ability, life is different if Campbell was Payton's successor. Then again, maybe all this hypothesizing is for nothing. There's no guarantee the Saints would have chosen the players' choice.