Saints could get to $14.61 million under the cap without restructuring Derek Carr, after Saints salary cap potentially increases by $5M

I think you're mistaking "rebuilding" for "tanking".
I'm not mistaking "rebuilding" for "tanking." I come from a family of contractors, carpeteners and construction workers. Remodeling one room in a house is not a rebuild to me. Moving on from the QB is not a rebuild to me. Like I said it's a subjective term that means different things to different people.

A rebuild to me would be turning over half the roster or more. Not just the QB.
If Rattler comes out with an exceptional and unprecedented 2nd year leap. It accelerate the timeline immensely to the point where you go right back into a building phase.
You're assuming Rattler would be the starter. Carr leaving doesn't necessarily mean Rattler would be the starter.

Cutting a quality starter that will win you games isn't a competitive move.
Which is why I don't think they will cut Carr and not bring in someone else. Moore and Loomis made it clear that they want to compete. You don't get the college record for most wins as a QB without an obsessive competitive streak.