Given that, as mentioned above, the phrases are essentially meaningless and just stand in for 'message ends', I don't really see why teachers harp on about it. It doesn't matter and I would certainly take more issue with someone who looked down on a correspondent who got it 'wrong' that the perpetrator of the crime.
I'm not a subscriber to the idea that good grammar and spelling serve no purpose - the rules have been developed over a long time to iron out ambiguities as much as possible and that's very important - but rules like this one are responsible for turning people off good writing, with the rules that do matter suffering as a consequence.
These things are just over my head. Why do I need to remember so many rules? Yours faithfully/Yours sincerely/Sincerely/Sincerely yours, and even sometimes people say Yours. So when I write to a person I even need to know whether the person is from USA or from UK?
Not necessarily.
Just hold to the rubrik that if you know the person's name (Dear Mr Smith), you end your Yours sincerely or even just "Sincerely". If you do not know the person's name (Dear Sir/Madam), you end with Yours faithfully.
If you know the person well (Dear John/Dear Mary), you can end with "Yours" or "Best Wishes".
I'm fascinated.
In American English, there's just one rule: only capitalize the first word.
We don't use the above phrases. We have four standard sign-offs:
Yours truly,
Sincerely,
Sincerely yours,
Love,
The first three don't mean anything and are interchangeable. The fourth is what is it is.
I'd never heard of Yours Faithfully. Glad I stopped in!
Yours faithfully and Yours truly carry the same level of formality, and are used here interchangeably by company/public officials writing to someone they have not previously contacted.
Very rarely now are the reversals used.
Even more archaic:
I remain, Sir, your obedient servant
and I receive a letter ending like this, I know that it must be regarded with great caution