AFAICS the answer a lot less simple than you seem to think, b/c it doesn't just involve adding a button. The desired behavior would require Q2A to suddenly treat a question with an answer like it didn't have an answer in the first place.
Besides, questions with no accepted answer already remain in the Unanswered tab, just not in the "No answer" subsection. You find them in the "No selected answer" subsection instead, which is 100% correct.