That’s where you’re wrong, my friend. The Constitution stipulates that the Chief Justice preside over the Senate trial when the President is impeached. That is the lone exception.
The VP was meant to be a backup, with so little actual responsibilty that it never occurred to the Framers he might be impeached.
The Constitution specifies that the president of the Senate preside over impeachment trials, with POTUS the ONLY exception.
I know, but come on. You don't think he doctrine of due process will prevent a person from sitting as a judge over his own trial? Besides, I think the SC has original jurisdiction over this, so a dismissal can easily be appealed.