While I agree with most of what you said, there are two additional key things not mentioned.
1-Where/what was the average field position on 4th down, when the Saints punted inside the opposing team’s 20? Was it at the 50? The opponent’s 45...etc?
2-On non-returned punts (fair caught), how far from the LOS did the punt travel? (IE; pitching iron distance punt, compared to a driver type distance punt, is a big difference). Shorter the distance, more likely a fair catch will happen.
I saw a number of his punts last season, where the offense stalled inside their own 30, and his punts were fair caught around the opponents 45, or even nearer the 50. And lot of times, he was kicking the ball out of bounds, between the 50-45 yard line of the opposition. This was a far cry from his previous abilities, when he was at his best!
All said. It is time to move on.