The OP is based, IMO, on a false premise, i.e., that ohnston was ready willing and able to confront Sherman's Army at a right opportunity, known only to Johnston.
Davis replaced Johnston because he could not get a clear answer to whether he would ever fight Shermans Army. If he was, he certainly did not inform Davis of any such ambition.
As noted by others on this thread, Sherman was tired of chasing the AOT to no good end. Part of the rationale for his March to the Sea, was Sherman's stated plan that such a movement would force Johnston(or later Hood) to either leave his entrenchments and meet Sherman in open battle to stop his March or, stay behind to to face Thomas' new Army, being formed to follow the AoT wherever it went, while Sherman marched against Georgia Militia to the Sea, and then to Peterberg.