Has anyone ever been asked to video record the client as they take their oath?
No, did someone ask for that???
I see no reason to do this. If you sign a jurat, you are assuring that you took an oath from the signer. I know of no state that does not require this. The law always presumes that an oath was given. Taking a mere signature and not taking an oath with it might render the document invalid.
Are you notarizing a document or swearing them in for a court hearing? I’ve never had to do this but I can see a court or attorney asking that this be done to preserve the integrity of due process and the legal proceedings.