Why did Alan agree that he could no longer be a cutter after revealing that he had an implant? He was already taking steps to stop his chip from working (the tattoos). Given that his chip wouldn't work in the future after he finished getting the tattoos, why couldn't he keep cutting?
He had already broken the cutters code, I don't think he had a choice after that. But I think the main thing was that he really wanted to revisit that childhood memory and the other two cutters would not helped him otherwise.
Oh, and he was getting fed up of the job (from what it appeared)... by that point his machine was all destroyed too.