Hello, PJ. The CJ is only required for the trial of a president - apparently to eliminate the conflict of interest of the VP. A former president on trial does not create that conflict.
So, if you think about it, this impeachment is really a Constitutional Conflict. What we have now is two Constitutional bodies in conflict: the Legislature and the Electoral College. The Electoral College did what the House of Representatives wanted to do.
The former is a permanent body and the latter is a transient one, but it is the latter that chooses the President and so has an enormous, but singular, power. They chose to not reelect the President, and Congress should accept that and move on.
The Electoral College shouldn't be minimized because of its temporary existence. It is a "thing in the Constitution" and is therefore "Supreme law of the Land." I won't go so far as to call it a co-equal branch of government, but it has a plenary power of its own and Congress and the Supreme Court should acknowledge it and stop this nonsensical impeachment trial as moot, since another Constitutional body already acted to achieve the intended result.
Pelosi and Schumer are just miffed that they won't get the chance to exercise the second penalty of impeachment because the Electoral College beat them to the first penalty.
-PJ
On further reflection, I believe this conflict still exists and warrants the Chief Justice to preside.
The conflict is that the sitting Vice-President would likely be the candidate in 2024 running against the defendant in this impeachment trial. Harris would be in the position to preside over the barring of her most feared 2024 opponent.
-PJ