There are two contrasting aspects to politeness. On the one hand we want to gain the respect of others, and on the other hand, we want the ability to do whatever we want without other people impeding us. So politeness involves both awarding esteem (positive politeness) and not getting in anyone’s way (negative politeness).
AmE employs more positive politeness. Being considerate and courteous involves including people and showing approval with warmth and friendliness. The stereotype of the garrulous American who gives you a run-down of their entire life history within five minutes of meeting them is rooted in this. It’s just not polite to hold back. You’ve got to show solidarity, share and be open.
Meanwhile BrE employs more negative politeness. Being considerate and courteous involves not imposing or intruding on people. The stereotype of the aloof, standoffish and reserved Brit is rooted in this. It’s polite to leave people alone so they can go about their business without your getting in their way.I’m using the terms ‘positive’ and ‘negative’ here in a technical sense. It’s not that American politeness is good and British politeness is bad. They’re just different, like electric currents can be termed positive or negative without being better or worse than one another. Both aspects of politeness are important in both cultures (and indeed all cultures). But we’re looking at a difference in weighting here.
I maintain that this difference is core to understanding how the UK and US came to be separated by a common language.