Exactly. The core purpose of a senate trial to remove a functionary from office. All that other stuff presupposes the senate had jurisdiction over such a case to begin with, which it wouldn’t.
The Democrats may come to rue their impeachments of Trump as setting precedents for a low standard of proof. If the GOP wins the House and Senate in 2022, impeachment of Biden and Harris for election fraud and other misconduct may well be on the table, with the GOP House Speaker to succeed as President if they are convicted.