I think the only business reason for him to not take a significant pay cut is if he thinks the Saints won't cut him if he doesn't take a pay cut. I think it's a game of chicken at this point.
That being said, Carr showed to be vindictive and hard headed when he left the Raiders so he might refuse to do it and force them to cut him and deal with the cap implications. But, I think it's a bad move for him from a business perspective.