He's there to confer an air of constitutionality on what is otherwise a show trial. He's window dressing.
So the word preside in the constitution has no legal effect?
The common use of the word implies the power to rule on evidence and objections. I believe the framers intended that the Chief Justice was to preside by issuing rulings on the admissibility of evidence and objections to questions.
But then the constitution has no meaning anymore.