This very British sentence cracks me up every time I hear it. This morning one of the guests, Walter, said “Melinda, would you be so kind as to bring some more coffee”. I answered “Yes, I would be so kind” and then chuckled to myself as I proceeded into the kitchen. I do not know why I think it is so funny. I guess in American English it is assumed that if you ask something of another, that person is “so kind” if he does it, so there is no need to add it to the original question.
On the other hand, maybe there is a higher percentage of positive actions to the British way, such as if you ask if the person “would you be so kind” as to do something, that person will be more encouraged to do it, as denial of the action would prompt the questioner to assume they are no “so kind”. ..