The drop-down caret is a convention on the Internet, but you’re absolutely right that a small percentage of people may be surprised it didn’t instantly publish. (Also, some may not know they can click it at all, since it not a skeuomorphic button, it is not #0000FF, and/or it is not underlined. Web design is full of such “compromises.”)
However, after clicking, the next step is clear, and everything is fine. In Don’t Make Me Think this is called a “kayak.” (Like how you* can roll over in a kayak and everything is fine).
*If you are a really good kayaker with the appropriate equipment.