You are assuming that Payton wanted him out, which may be true, however, it could have also been the other way around.
In German we have a saying: Reisende sollte man nicht aufhalten.
Loosely translated: Travelers should not be stopped (on their journey).
Evero might have first emotionally moved on in the moment Hackett got fired, see his refusal to become interim HC, and at the very latest when he did not get selected to become the new HC.
He was by far everyone's preferred option as DC yet this now might be an inevitable fresh start for everyone.