No, I’ve never seen or used “Yours faithfully” here. I do not recall it being taught.
With email and the informality that it brings, “Yours truly” is probably sounding more stilted as time goes on. But it’s interesting to see how much more floridly letters used to be signed. I was struck by the way that opposing generals during the time of the American Civil War would sign communications to each other:
Confederate General Hood wrote in a missive to U.S. General Sherman, “And now, sir, permit me to say that the unprecedented measure you propose transcends, in studied and ingenious cruelty, all acts ever before brought to my attention in the dark history of war.” Yet he concluded with, “I am, general, very respectfully, your obedient servant, J. B. HOOD, General.”
And Sherman’s response, which includes “You who, in the midst of peace and prosperity, have plunged a nation into war–dark and cruel war–who dared and badgered us to battle, insulted our flag, seized our arsenals and forts that were left in the honorable custody of peaceful ordnance-sergeants, seized and made “prisoners of war” the
very garrisons sent to protect your people…”, is signed with, "I am, very respectfully, your obedient servant, W. T. SHERMAN, Major-General commanding.
(By the way, learners of English looking for good reading material, especially if they’re interested in history, could do worse than to read the memoirs of generals William Tecumseh Sherman and Ulysses S Grant. They are both very readable and very interesting. And they’re available for free at gutenberg.org)