The constitution allows this.
No it most certainly does not!
Article I
Section 3
Clause 6
The Senate shall have the sole Power to try all Impeachments.
When sitting for that Purpose, they shall be on Oath or Affirmation.
When the President of the United States is tried, the Chief Justice
SHALL preside: And no Person shall be convicted without the
Concurrence of two thirds of the Members present.
"SHALL" means he must preside over an Impeachment Trial.
Shall is ironclad. It's not the same as may, or might.
He’s not president!!!!!!! That’s why they can do this.
If I may jump in with a comment on your post 52.
Any Chief Justice could reply to your argument that the SHALL applies to an Impeachment trial for which the remedy upon conviction is a removal from office. In this case the subject of the charge is no longer in office so such a trial is moot.
Playing into the Democrats hands he backs away without declaring, in his Constitutional capacity you cite, such an Impeachment trial invalid and therefore the House gets a complicate Senate to play a charade and for the purpose of a Trial that is not a trial, they use Leaky Leahy.
Since the House Impeachment did not follow the rules, why should the Senate. Its the District of Caracas, not the District of Columbia anymore. The press won’t object they just play along like the show trials for Stalin.