You don't take turns, though. You can act as long as your active time meter is full.
Most games don't allow you to constantly attack. Even action RPGs sometimes don't let you constantly attack, there are often delay periods on your moves, or cooldowns on special abilities. That doesn't make them turn-based, either. The menu-drivenness of ATB games seems to always trick people into thinking they're turn-based, for some reason. I guess because they equate "command menu" with "turn-based."
ATB is as turn-based as the combat in World of Warcraft or Final Fantasy 11 is. Both rely on cooldowns before you can act again, even with regular attacks. FF11 is even menu-driven just like ATB games are. The only differences between FF11's combat and ATB are that you can move freely around the battlefield in FF11, and in FF11 your moves have cooldowns on each ability instead of for your next action. And in fact, FF10-2 and FF4 DS added the variable cooldown aspect.
In Japan, these types of games are called "command RPGs," which I think is a much better descriptor for the umbrella that includes all of the FF games, Grandia, Dragon Quest, etc. Turn-based refers to games like FF1-3, FF10, Dragon Quest, Blue Dragon, etc. where nobody can act until the person whose turn it is has acted.