Brees isn't throwing deep because he can't and hasn't been able to going back to 2017. Zimmer knew it and has been scheming with that in mind.
With as many games as Teddy started, and without the arm strength issue to compensate for, I find it dubious that a Coach of Payton's caliber wouldn't try to add the deep threat dimension. Ginn is still there as well as some young guys that can get deep.
I watched 3 of Teddy's starts and I saw a healthy version of the same guy we saw in Minnesota. He'll go deep on occasion but 95% of the time his fist instinct is short to intermediate. And there's nothing wrong with that.
My preference will always be for guys who look deep to intermediate and then take the short pass when needed. Cousins is by no means perfect on that regard but he sure as heck looks deep way more than Teddy.
It's a philosophical thing. Chunk plays equals less plays you need in a drive to get a score. Which equals less chance of a drive-killer like a TO, sack, penalty or negative yardage play. Mike Zimmer prefers to bend and not break on Defense instead of attacking because he believes your Offense will make that mistake more often and kill drives instead of scoring.
My personal preference is to attack on at least one side of the ball. Kirk takes shots. And deeper shots with better spin, trajectory and placement than Teddy. But he's not reckless with it like Case was, who seemed to have an aversion to taking 5 free yards on a checkdown to a wide open RB in the flat.
I still root for Teddy but he's a better fit for teams like Buffalo that are conservative on Offense and attack on Defense.