Could Derek Carr be a post-June 1 cut?

The theory is he would do it to help himself get in a better situation, not help the Saints out. But like I said they'd need to be another team out there willing to cover his base salary (BEFORE FREE AGENCY START), very unlikely.

I don't see any situation where Carr helps facilitate a trade for even a 7th round pick.
He might not like the next Saints HC.

I don't think he would do it to be a backup, but there are a few teams where he might start that need a QB, but don't have an replacement and might not like this years draft class and/or not be in a position to draft one. Such as the Colts.