This isn’t courtroom rules of evidence. It would be messy, but the House can define just about anything they want as “high crimes and misdemeanors,” based on the original discussion of that term, and they MIGHT even try treason, based on the original definition of that term for impeachment purposes (read:Russia). Right? Fair? Decent? None of those are required. This ain’t court. Don’t rule it out too quickly.
"Ye hear of wars in far countries, and you say that there will soon be great wars in far countries, but ye know not the hearts of men in your own land."