I didn't actually ask a question, I just made a comment.
[Executive Branch] Article II, Section 4 states:
"The President, Vice President and all civil Officers of the United States, shall be removed from Office on Impeachment for, and Conviction of, Treason, Bribery, or other high Crimes and Misdemeanors."
So if the Senate convicts, removal from office is automatic, not an option.
[Legislative Branch]
Article 1, Section 3, Clause 7 states:
"Judgment in Cases of Impeachment shall not extend further than to removal from Office, and disqualification to hold and enjoy any Office of honor, Trust or Profit under the United States: [snipped part that doesn't apply to impeachment]
"
So after conviction, the only thing the Senate can consider is a disqualification for holding any office.
So I'm still yet to be convinced that the Senate even has the authority to remove former presidents from an office they no longer hold. If they don't have the Constitutional authority to convict and remove someone from an office they no longer hold, they certainly wouldn't have the authority to impose such a disqualification from holding future office onto a private citizen.
Only 20 officials, including only three presidents, have been impeached by the House in all of American history. And, of these 20 impeached individuals, only 11 were either convicted by the Senate or resigned their office after they were impeached but before their Senate trial.
And only in 3 cases did the Senate go ahead and take the step of permanently barring convicted impeached officials from holding future office (they were federal judges in all 3 cases).