Saints fired Dennis Allen

Loomis probably felt there was an optimal financial, structural (league calendar, et al) time to fire DA

Gayle, players other coaches had a more immediate social, cultural, emotional timetable they were working with

both can be right from their POV - Loomis just got outvoted and is trying to signal to potential coaches that they'll have a cushion of time to effect change

Yep. Loomis even mentioned in the NOF interview that he thinks one of the reasons this is an attractive job is because this is a "first class organization" with a good reputation around the league. I think he thinks part of that is that it's a team that tends not to fire coaches mid-season, gives them time to prove they deserve the job, and does whatever they can do financially to give the coach the team he wants.