Rizzi should be the permanent Head Coach
Usually these assistant coaches who have been around the block a few times tend to build some reputation and friendships with other coaches they have met & worked with along the way. They also begin to develop a philosophy about what makes for a successful team. But few (if any) of these interim guys get to fully implement the vision they want for the team unless they eventually get the head coaching job without the 'interim' label.
Rizzi is where he is today because he has applied what he learned and has preached to his players what he believes will work. If, over the time he was worked in this organization, Rizzi really has seen areas of this team and staff that requires the kind of changes to fit his philosophy, then he will attempt to make these changes where possible. But I don't see the organization giving him the keys to a complete resetting of staff and players. Only proven (or VERY promising) head coaches get to have such carte blanche as part of their agreement to take over the reins of all 'team related' responsibilities and activities.
The best Rizzi can do is to try and get the personnel that is already on-board to buy into his way of running the show. If an assistant coach (or even a player) willingly balks at the changes he wants to make, then he will likely have to take up the issue with the front office. But it is highly unlikely that any major changes will take place for the remainder of this season. So I really don't believe that we will see a true vision of what it would be like to have Rizzi as our new head coach unless the front office gives him that opportunity for a few seasons.
The best that Rizzi can do in the next two months is to raise enough eyebrows (both inside & outside the organization) to make himself a legitimate candidate to be the next official head coach of the Saints. But the chips are definitely stacked against him. That is unless the plan is to keep him on for as long as it takes to get the dead salary cap money back in order. However, it would be hard for the Saints to pull off such a plan without making it obvious that he is just a lame duck coach who is keeping the seat warm for the eventual successor.
Winning football games is the key for Rizzi. Nothing would speak louder about his leadership and coaching prowess than turning this shell of a team into a disciplined and well-oiled machine that can actually produce victories on the field. While the task is daunting, he does have a few things in his favor.
One is that the players still want their jobs and they will (likely) appreciate the new direction of the team. There is new motivation for everyone to go to work in the morning. Two... the opponents have to plan for an unknown philosophy and a coach that is basically playing with house money. While 'football is still football', there is something to be said about going up against a team that has nothing to lose except a better draft position. And three... no one is expecting him to be the savior of the season or the team. Everyone knows that the Saints will not 'shock the world' and get a ticket to the postseason. In fact, some are even openly hoping for a 'draft elevating' crash & burn for the 2024 season. The only pressure he will have is whatever he puts on himself to right the ship.
It's very possible that by this time next year few Saints fans will even remember coach Rizzi's name. But if he IS able to work miracles with what's left of this transition season, it would be a crime if he didn't at least be given some consideration to permanently take over the job of making the Saints a team that we can all be proud of once again. The next eight games should be interesting to say the least.