For the MLE, it'd be a questionable move when we're in such dire need for big men. And though we could trade Green if we signed Carter, we wouldn't exactly be in the driver's seat. Teams could simply just try to sign Green if they really wanted him; furthermore, in a trade, teams could attempt to rip us off for Green knowing how desperately we'd likely need a backup 5 with the MLE off the table.
For the minimum, it'd be a no-brainer. Sure, he has his flaws, but the guy can still play. And for a team that had the trouble scoring the basketball when the starters went to the bench, he'd go a long way in helping in that department.