What we have seen from Wise is that he can be an effective part of a rotation in certain roles, but he lacks the versatility we have come to expect as a patriots IL. He has value to the team as a situational interior rusher, but has been a disappointment setting the edge as an end in the 3 - 4.
With the additions of Godchaux, Anderson and Judon the defense looks positioned to continue in a 3 - 4 alignment. If roster conditions force Wise to be a starter in these looks, he will likely disappoint again. If the team is able to bring back Guy, or Allen returns and rises to the occasion, then Wise can effectively play Butler's role as a pass rushing interior lineman in nickel and dime looks.
My guess is that carrying Wise and Butler has proven itself a roster redundancy, and that the team has settled on Wise as a lower cost option.