I actually didn't like Final Fantasy XI's chat window, because of the fact everything was in one window. I rather like multiple tabs, but I do believe Final Fantasy XIV tabs are-- a bit.. half-hazard?
One there is no good way to swap through tabs unless you click on it; so It needs a keyboard command that way you don't have to reach up there with your mouse and go: "I want this tab up."

Secondly I know a very, very old game that pre-dates World of Warcraft that also uses the Tab system (has been since its creation) and it actually does a better job because it allows you to decide one thing i wish Final Fantasy XIV would allow you to do.

How many tabs do you want on any given window and what do you want those tabs to do?

In this particular game (Istaria - formally known as Horizons: Empire of Istaria), it starts you with 2 windows. One for all the chat, one for all the combat. By the time I get a hold of it. It has one window, with maybe up to 4-6 tabs to break stuff down so I can quickly glide over different things. It also pops up a new tab when I get a whisper (or window, if I tell it to do that).
When a tab gets a message, it sits there and flashes at me saying: "Hey look at me."

Another game that has a rather intelligent tab function is also CoX(City of Heroes/City of Villains) as a more modern day example. Though it takes a bit to hassle with it.

So there is nothing wrong with them using game tabs in my personal opinion, but they do need to make the chatbox a bit smarter and a little more customizable friendly. That way perhaps by the end of the day, everyone wins.