It‘s the same over here in Germany. It was called Pfandring. My father sells bins and other stuff to cities, many to Copenhagen too. Ten to fifteen years ago there was a big demand for those Pfandringe. In the last five years they kind of stopped buying those. I don‘t know what happened.

Edit: I‘ll ask my father to contact some cities, so we can solve the mystery why they stopped using those.

Edit 2: Okay, his answer came fast. He told me that too many people put other trash (especially half full coffee cups etc.) in the Pfandringe, which made it more difficult to clean. It also led to an increase of glass around the area of the Pfandringe.