Derek Carr practiced today.

That's easy to say, but how many coaches/QBs have the other teams in the NFCS gone through since Payton/Brees came to the Saints? What were the Saints like in the decades before Payton? Like it or not, except for a few elite teams, this is the norm in the NFL. And if you go by history, the chances of a new coach having the same results as DA is a lot more likely, by a lot, than finding someone like Payton. Superbowl level coaches don't grow on trees.

Not that the Saints shouldn't bother looking at other options, but just changing coaches doesn't necessarily get us back to the good old days.
Since 2006:

Atlanta — 7 head coaches (2 midseason interim HCs)
Carolina — 7 head coaches (3 midseason interim HCs; 5 HC changes since Tepper became owner)
Tampa — 7 head coaches (0 midseason interim HCs; 1 late offseason resignation)

New Orleans — 6 years of Payton, the bunk 2012 suspension, 9 more years of Payton, then Payton’s semi-late offseason resignation.

Double-digit loss seasons since 2006:

Atlanta — 6
Carolina — 8 (incl. an active 5-season streak)
Tampa — 8

New Orleans — 1, and they lost in week 18 to get there. It took a 17-game season for it to happen.