I don’t do it often either, but I occasionally do and this is a nice addition. But there’s another more common use:
There’s an issue with the iPhone version of this site where the regular “quote” just pastes at the bottom of your draft message instead of where your cursor is. So you then have to select and cut out the quoted item and paste it where you need it to be. With the copy quote function, you can paste the quote exactly where you need it to be in your response.