Actually, I think the concept itself conceptually and linguistically may be at a crossroads as we speak. I think the Founders thought the concept central to the United States.
I am not a scholar on the subject, so I'd like to toss the notion out to get people's thoughts on the matter, but the notion of "impeachment" seems to me likely intimately ties up with honor.
We tend to think today of impeachment as removal of an official from office, but that doesn't see to be the case, does it? I suspect that the original idea behind impeachment may have, sadly, feel a bit foreign to us today. What has been impeached may not have been the official, but the official's HONOR, with general agreement by the officials peers and superiors, depending of the official's rank.
Duels were fought at that time over honor. Such a stunning mass indictment would probably at a minimum force an official to leave office with a shocking loss of face. Suicides have been known to happen over less. Such a punishment could hardly have been more severe.
Thoughts today about the notion of honor itself, the honor of specific government officials, and the honor of the government as a whole seem to have shifted enormously over this time. I don't know if it's for the better or for the worse overall. What Auden said—was it about the '50's—about it being "a lowdown dishonest decade" are as chilling today as they were then, aren't they?