Shall We Dance?

A long time ago, it was common but not now. It was the language of kings and kingdoms - very formal, very old.

The only people who use it now are service people at NICE hotels, restaurants or other luxury services or shops. It has a very royal atmosphere - "The customer is king."

Nowadays, a better expression is "Would you like me to...?"

Michelen star french restaurant - watier: "Shall I bring the wine list, sir?"
Ritz Carlton - front desk: "Shall I call a taxi, sir?"

Average to semi-nice restaurant: "Would you like more coffee?"
Average to semi-nice hotel: "Would you like me to give you a wake up call?"

Business case, talking to a client:

Bad!: "Shall I send you a sample of our product?"

GOOD!: "Would you like me to send you a sample of our product?"

"Shall We Dance" is a good use of "shall" because ballroom dance is a very elegant, upper class activity (that wealthy, rich, powerful people used to do.)

「shall we dance」というのは、「おどりましょうか」か「おどりませんか」の意味です。尊敬語のような英語です。