DEAR MISS MANNERS: I worked for a bank for many years. We were required to greet customers as soon as they entered the door.
The reason was very sensible: Bank robbers do not want to be recognized. They assume, correctly, that if you see them before they terrorize you, you will be able to describe them. What does Miss Manners think?
GENTLE READER: She has no objection to polite methods of ferreting out potential criminals. Miss Manners only hopes that the greeter keeps the intrusiveness of his greeting below a point that might terrorize the customers.