I always assumed soft drinks weren't shown on Star Trek because of product placement reasons, much like having certain kinds of rock music would date the show. But considering how Quark once mentioned root beer, it was always there, lurking unseen in the background.
Well, there are ways around product placement which many TV shows often do and Trek has done in the past. Next time you're watching Enterprise's Carbon Creek, pay close attention to the ketchup and mustard. Although it looks like the Heinz label, you'll notice the brand name written on it is in fact Fines.
Ignoring time travel episodes the first indication we get that people still drink cola in the future is Enterprise's Terra Prime, and even that is just on a list of drinks. The only time cola gets a direct mention is the second last time to feature the Prime Universe. Personally, I find that shocking.