To complicate, certain uses of reflexive pronouns are standard in Hiberno-English, eg. 'Is himself inside?', 'Good man yourself!' and 'Is it yourself?' (which is more or less a phatic greeting, rather than a question.)
Though I agree that the 'it is more formal-sounding, therefore I should say it to sound important' usage is fairly annoying -- I think of it as a The Apprentice usage, because it was the first place I came across it a lot, a few seasons back, when all the hapless numbskulls brought back to the boardroom would bleat in response to questions 'That would be myself, Lord Sugar.'
This is from Stan Carey's brilliant language blog:
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Reflexive pronouns are very common in Irish English, often used for slight emphasis, e.g., “Good man/woman yourself”, “Ah, ‘tis yourself!” There are a few examples at the foot of this page:
“
“An’ is it yourself that’s there, Mikee Noonan?” said the one first introduced to the reader.
“Indeed it’s myself and nobody else,” said Noonan
(Samuel Lover, The Burial of the Tithe)
And here:
“
“You know yourself ‘tisn’t lucky to postpone a wedding.”
“’Tis herself was picked, so no other’ll do.”
(M.J. Molloy, The King of Friday’s Men)
As well as being used this way, herself and himself also serve as informal terms for “the wife” or “the woman of the house”, and “the husband” or “the man of the house”, respectively. It’s a colloquial way of mentioning someone casually, respectfully, and perhaps with a little mild, affectionate mockery. A character in The Irish Twins says, “Come along to my house this afternoon, and listen to Himself telling about the States!” You can imagine eyes rolled or eyebrows raised in knowing amusement in the delivery of that line.
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'Himself' or 'herself' is more or less equivalent to the English affectionate informal usage 'him indoors' or 'her indoors', in fact.
Anyone who's interested in language should have a look at Stan Carey's blog -- this is a good entry on descriptivism vs prescriptivism
stancarey.wordpress.com/2010/02/16/descriptivism-vs-prescriptivism-war-is-over-if-you-want-it/
and this is the one this thread reminded me, on 'compulsive pedantry' in Ali Smith's How To Be Both:
stancarey.wordpress.com/2018/03/28/compulsive-pedantry/#more-24519
but the whole blog is endlessly interesting and well-informed.