Earlier quoted context omitted.
except that you can't know if the person who is typing is the real one
That's why I said part of that step could happen before the flight. You would also want to have some tests in person for the people who made it past the remote test. They probably wouldn't be needed that much, though, because I don't think most applicants would go so far as to have someone else type their answers if they were doing it live on the phone with someone from the hiring co.
yeah, on a second thought in the potential to limit the stress I suppose this could be used by putting the intervwee alone in a different room and watch them code remotely from another room.