chief justice Roberts should not allow them on it knowing they spurn their duties.
This is an interesting supposition. While I don’t think a ruling would be made to uphold this idea I actually think there is a sound constitutional test here and that is always worth a review.
While the constitution does not have any reviewable clauses concerning impeachment, itself, there is certainly a reviewable clause concerning the trial. Namely that there shall be an oath or affirmation. If the senate failed to take an oath before an impeachment trial that trial would not be constitutional. No doubt it’s a constitutional obligation.
The reason for the oath is because impeachment is a very serious responsibility of senators - alone - as it is an important check on unfaithful public servants. Senators shirking this responsibility is theoretically unconstitutional.
Now, Chief justices have pressed their will on senate procedures before and they have been overturned by the senate and it was ruled that the senate should govern themselves in impeachment trials but technically is an oath part part of trial procedure or is the oath required before trial is really the question.
Constitutional law and statutory law are two different things and I don’t like to compare the two but a good analogy would be does a trial begin at the jury selection?
It should also be noted some senatoyon the past have argued they are not qualified to be jurors in such matters but that was dismissed (I forget how, whether internally or at SCOTUS) but the end result of that was all senators must fully participate in trials.
Still, it’s an interesting test.