I would like to hear from the forum regarding the use of 'sir' in American literature, such as 'The Manhattan Transfer' by Dos Passos published in 1923. In the Italian translation it is given in the extremely formal 'voi' form, and I would argue that there are numerous examples of 'sir' in that period of American literature where it could be read as being an informal 'tu', simply replacing a name or title where that information is unknown.
Note this entry from Vogue's Book of Etiquette, 1925 (emphasis mine):
A dinner-jacket used to be the sign of extreme informality in the evening. A man might put it on for dinner at home and change it for a dress-coat if he went to the opera or a dance afterward. Now it has become so usual an evening garment that, except on most ceremonious occasions, most young men wear it habitually.
Also note these definitions of sir from Merriam-Webster:
: 1 a : a man of rank or position; b : a man entitled to be addressed as sir
: 4 -- used as a usually respectful form of address
I would argue that sir could not currently be renderered as tu, and certainly not in an era that considered a dinner-jacket the height of informality.
It depends on the context. For instance, in a formal letter:
Dear Sir or Madam: I am writing to complain about your restaurant service...
As FumbleFingers pointed out:
You, sir, are a bounder and a cad!
The 'sir' is an ironic use of the formal in a derogatory fashion.
Then there's also:
You, sir, are a gentleman and a scholar.
The 'sir' in this expression is a also somewhat ironic, but more of an informal, joking fashion.
I have no idea how you translate any of that into Italian, and that would be off-topic for EL&U anyway, but I think it illustrates that 'sir' can run the gamut of formality.