Reddit reviews Debrett's New Guide to Etiquette and Modern Manners: The Indispensable Handbook

Only the nicest guys blame the murder victim. That's how you can tell they're old timey gentlemen! It's straight out of Debrett's:


"If a young lady has been murdered by Chad, call her out for the dumb slut she is. Make sure you do it where everyone will see. Manners maketh man, after all!"

The valedictions in question never truly fell out of use, but have become abbreviated instead.

Valedictions in English writing have traditionally been very formal affairs following the French model. You can still observe similarities between 18th c. Georgian English valedictions and their modern counterparts in French:

My Lord, Your lordship's most humble, most obedient servant, Sam. Johnson, "Letter to Lord Chesterfield," Samuel Johnson, 1755

Nous vous prions d'agréer, Monsieur, nos salutations distinguées, Modern French, Calliope Source

English has long had a tradition of abbreviations although valedictions, as a piece of formal writing, withstood most of them until the 19th century. These long valedictions were eventually whittled down to the common form we see today:

• "I remain, Sir, your faithful and obedient servant" / "Yours Faithfully"
  
  There remain a few, rare times when the full English valediction is still employed. Diplomatic correspondence tends to be very formal indeed and it was considered good manners to conclude letters to ambassadors and Governors-General in Commonwealth realms with the full valediction until the early 1980s. As of 2000, Debrett's still mentions the full valediction although it described it as somewhat "old-fashioned" even then, so it may be totally out of use today although I wouldn't be surprised if it was still used sparsely in official documents between the Foreign Office and accredited ambassadors to the United Kingdom.