Please allow me to explain that a Hechsher is not a logo. It's a certification that a product is kosher. Just because Coke may not necessarily have an OU logo on it, that doesn't mean it doesn't have a Hechsher. In fact, the production was fully supervised by the OU and the beverage indeed has a Hechsher, which just happens to not be listed on the label. This can only be said about Coke from the US, all of which are certified by the OU. It cannot be said of Coke in other countries, where only certain facilities are supervised.
That said, Coke needs a Hechsher. It's not like plain coffee or tea which don't need one. Coke does contain many sensitive ingredients, whereas coffee and tea contain just coffee or tea.
I really hope I was clear this time around.