Babylon has risen and fallen several times.  Let's take a look.....

1st Babylonian Empire - Genesis.

In Genesis/Beresheet, Babylon was established and men tried to make it the dominant city in the world.  God squashed the idea and scattered the people.  That was the first rise and fall of Babylon.

2nd Babylonian Empire 1900-1595 BC

From 1900-1595 BC, the Amorites established Babylon as the capital of their world power, and they conquered many other nations.  That came to an end in 1595 BC when the Hittites conquered Babylon and Babylon because subject to foreign rule from then until 629 BC, changing overlords in 1158 when the Assyrians conquered them.

3rd Babylonian Empire 629BC to ?

The Amorites re-established Babylon and not only became independent at this point, but conquered Jerusalem as well and conquered many other nations.  Babyloned weakened, losing its grip on other kingdoms, and finally dwindling to nothing.  They never conquered the entire world and one could argue about exactly when they went from a great power to a mediocre one to not much.

4th and Future Babylonian

The biggest argument against literal Babylon being "Babylon" is that as of today, it is desolate.  Big deal.  They've been there before and risen back to the top dominant world power twice.  There are many signs the False Messiah will rise from Rome, and later will....

"...plant the tabernacles of his palace between the seas in the glorious holy mountain" (Dan 11:45)

this could be ancient Babylon.  It doesn't have to be.  But it is somewhere in the Mid-East, and where more poetic than ancient Babylon?  I think Babylon will go from nothing to the dominant world city again BECAUSE the False Messiah decides to move there.

Shalom, Joe