In "1776", the Continental Congress bangs on their desks as if to say "Hear, hear!" or to applaud. They do the same in the cabinet meetings in "Lincoln." I've never seen this happen in a modern political debate or as far as I can remember, any other context. When did this die out? Are there notes at some period of people saying it was uncouth or something?
To answer the first part of your question. It’s a essentially a substitute for applause in British Parliamentary Style Debate rooted in the British House of Commons procedures where the audience banging on their desks while someone is giving a speech is a sign of agreement and lets the speaker know which points are resonating with his audience. The speakers have limited time so by the audience knocking on their desks it gives the speaker a que on which information is resonating. Alternatively for the audience to express displeasure you can call out, “Shame!” or “For Shame!” usually if the speaker makes an immoral or unethical claim during debate although etiquette requires you not to heckle excessively and you can be removed if you are being excessive.
It is still used both in Parliamentary Style Debate and Lincoln/Douglass Style Debate, which are the two major forms of debating taught in American university classes and debate leagues. It’s also still used in the British House of Commons to this day.
I will ask my Professor as to when it died in American politics when I go to my Argumentation and Debate class on Wednesday. We are currently learning the history of Parliamentary Style Debate. If that doesn’t qualify then I can source my texts when I get home.
TL;DR: Americans got it from the British who use it in the House of Commons as a substitute for applause/agreement.