They could just keep the glassware in the freezer. That would be more efficient, more practical and save time but ...
It's all about the ice, about the ice, about the ice. It looks cool (pun intended) in the glass and is part of the ritual of authentic cocktail making.
I just wish they did not have to throw it away!
Photo: Robert Rath, 'It's all about the Ice', 1/30s f/1.4 ISO640 50mm