It seems to me that Britain has quite a bit more of this type of protocol than the USA, for the simple historical reason that the USA abolished the aristocracy and established a republic while Britain never did.
The historical and cultural reasons are clear to me: Britain has an unelected, hereditary monarchy that historically held final authority and had people killed if they weren't subservient enough. (To be fair, England's experiment with republicanism was no less tyrannical.) Over time, more and more checks grew against royal authority until eventually they grew powerless in reality. There even seem to be a few practical benefits from having the same titular head of state for decades, since most sources agree that the Queen provides intelligent and thoughtful advice to her Prime Ministers. It's a role that most parliamentary republics have replicated, albeit in an elected role.
But there was a time when addressing a monarch by the phrase "I have the honour to be, Madam, Your Majesty’s humble and obedient subject" actually meant what it sounds like. In practical terms, maybe royal protocol isn't a real problem. Maybe people tend to create their own royalties and aristocracies without the presence of a real one. But no, I wouldn't do it like that, though I understand and appreciate that it seems to work for Britain.
The historical and cultural reasons are clear to me: Britain has an unelected, hereditary monarchy that historically held final authority and had people killed if they weren't subservient enough. (To be fair, England's experiment with republicanism was no less tyrannical.) Over time, more and more checks grew against royal authority until eventually they grew powerless in reality. There even seem to be a few practical benefits from having the same titular head of state for decades, since most sources agree that the Queen provides intelligent and thoughtful advice to her Prime Ministers. It's a role that most parliamentary republics have replicated, albeit in an elected role.
But there was a time when addressing a monarch by the phrase "I have the honour to be, Madam, Your Majesty’s humble and obedient subject" actually meant what it sounds like. In practical terms, maybe royal protocol isn't a real problem. Maybe people tend to create their own royalties and aristocracies without the presence of a real one. But no, I wouldn't do it like that, though I understand and appreciate that it seems to work for Britain.