The Common Sense Case for Post-Presidency Impeachment/Trial

There's quite a bit of back-and-forth in the legal and political punditspheres regarding whether a public official can be impeached (or, in the case of President Donald J. Trump, tried pursuant to impeachment) after leaving office.  Rather than try to round it all up, I'll just point you at Keith E. Whittington's musings over at The Volokh Conspiracy.

I'm going to take a stab at the question myself, but instead of analyzing the constitutional text as a legal document or whatever, ,I'm just going to draw what seems like a common sense conclusion vis a vis original intent from Article I, Section 3:

Judgement in Cases of Impreachment 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 ...

If an impeached official couldn't be impeached, convicted, and punished with future ineligibility after leaving office, all that official would have to do to enjoy de facto immunity is resign any time impeachment and/or conviction looked likely. He or she could then keep turning up like a bad penny. Just keep a suitcase packed and run off to start the next campaign every time impeachment/conviction loomed.

At the presidential level, terms limits would be a problem these days -- but at the time the impeachment clause was framed, there were no such term limits.

So, did the framers of the Constitution intend for the the consequences of impeachment and conviction to be so easily avoidable that two words ("I quit") would suffice to defang the whole process? I doubt it.