As a surgeon, when you operate a suspected appendicitis case and found that it wasn't, do you still remove the appendix?
Absolutely! 1) Appendicitis can be a very bad disease & the appendix serves no critical purpose (as far as we know), so removing a healthy one poses no risk other than extremely tiny risk of wound infection. 2) It would be irresponsible to send someone off with an appendectomy scar whose appendix was still inside: the risk of misdiagnosis should bona fide appendicitis occur & the patient not remember whether the appendix was in or out would be unwarranted.
That said, in all my years of practice, I saw only one case of appendicitis in which we could not remove the appendix immediately, so we had to leave it for another day. I was assisting another surgeon operating on a 14 year-old boy whose appendix had ruptured & abscesses. The surrounding inflammation was so intense that anatomical structures were impossible to see clearly, so it was unsafe to proceed for risk of damage to them. We brought him back about four months later to take out his appendix & ALL the tissues looked NORMAL!-a testimony to the body's healing ability. There was no residual of the previous severe inflammation. We removed the appendix & he did great.