Key, McCullum and captain Ben Stokes breathed life into England’s Test team when they took over four years ago in the aftermath of a 4-0 defeat in Australia.
But the methods that brought 10 wins from their first 11 matches in charge have come under intense scrutiny in Australia.
The tourists have been far behind Australia with bat, ball and in the field. Their preparation has been questioned, including the lack of a full-time bowling coach or a member of staff with a speciality in fielding.
Heavy defeats in Australia often result in sweeping changes to the leadership of the England team, a move the ECB hierarchy are keen to avoid this time around.
However, the future of McCullum in particular appears to hinge on his willingness to accept the need for change and his ability to enact it.
“Whatever you do in life, you have to have some authenticity,” said McCullum.
“For me in the job as coach, you need to have an influence over how the environment runs and to be in charge of a lot of those decisions that are made when the pressure is on.
“So as long as that remains, I’m open to progress. I’m open to evolution and some nipping and tucking, but without being ultimately able to steer the ship maybe there is someone better.”