I recently watched 2008 movie "Babylon A.D.". The story reveals around a new mankind generation born. But why was it titled "Babylon A.D.". Here is wiki page for the movie. But even it didn't cover the answer.
Science fiction appeals because of the mind-expanding quality, bizarre and unexpected scenarios in plausible ways. This often includes disorientation re: space and time, for example, in Planet of the Apes the planet turns out to be Earth, after the title implies some other world.
Babylon A.D. also has a stop-short quality: if it doesn't quite make sense, that's the point. "Babylon" usually refers to the distant past or, as you say, the generic sense. "A.D." is both final and futuristic, not what we expect, this is neither the historical Babylon nor a generic reference. (If "C.E." is gradually being adopted, that adds to the effect.)
Playfully bewildering titles aren't uncommon in fantastic films. One I've found intriguing is the U.S. title for Quatermass and the Pit (1967): Five Million Years to Earth. A few years later came Dracula A.D. 1972, and The X-Files did "Hollywood A.D."
Thus, "Babylon A.D." seems less a plot reference (I haven't seen it) than an appeal to the tastes and cultural memory of s.f. viewers.