What about arthroscopic knee surgery on a knee that has been totally replaced?

Most surgeons will avoid to do this as an arthoscopy always carries a risk of infection, and infection in a joint with a prosthesis in it, is disaster. Besides of this, it is harder to do as the space is very thin after a TKP, and in most cases, there isn't much that can be done arthroscopical in such a knee anyway. After a TKP, you generally (but not always) no longer have any cruciate ligaments or menisci, so what are you going to perform arthroscopic surgery on? There are exceptions of course, but generally speaking, arthroscopy on a TKP is rare.