Gestures of courtesy aren’t confined to royalty or even the ‘upper’classes.
In the days when all men wore hats of some sort or another, they tipped their hats or caps at people they knew, whether men or women.
‘Howdo?’ was a commonly heard greeting in my childhood which accompanied the lifting of the hat. Just for the record, I grew up in a working-class district of Stockport.
When we’re out walking or cycling, people will often nod and smile. When we’ve been in America, complete strangers will smile and say ‘How ya doin’?’
It’s just a part of the human interaction that gels society.
Bowing and curtseying, as well as signifying obeisance and loyalty to the monarch, whom we have until someone thinks of a better system, is simply the top-end, most formal type of greeting.
Personally I object far more to being expected to hug and kiss people I barely know.