Babelfish? LOL
I know, to create completely new languages all at once would definitely require some serious brain rewiring for thousands of people all at once! The "program" for language is so genetically based that they can find certain learning disabilities that affect speech just by examining and small group of genes.
I think the "confusion of languages" story is another allegory. It's well known by linguists that the Indo European base language developed and spread through the Bronze Age like wildfire. One can almost trace the spread of those people by the languages and cultures they assimulated by studying the changes and branches in that language group.
It's thought that because these people first developed a few very crucial factors in advanced warfare, the taming of the horse, and the wheel, plus the smelting of metals for weapons, they basically assimilated a lot of more peaceful agricultural cultures in their advance.
We know that because the words for "wheel", "horse" "bridle" and "bronze" first appear in the Indo-European language cluster, for one thing, before many other root languages. The words for those things are grafted into other languages and adopted from the root of Indo European language, too, meaning these cultures borrowed that idea and technology from the earliest of the Indo-Europeans.
From that base language which linguists call PIE, Proto Indo-European, we first see Old Assyrian and the Hittite language, written in the very earliest forms of writing, cuneiform.
Soon, we have Hellenistic Mycenaean Greek (or Proto-Greek) then boom, Early Persian, Proto-Latin Italic (which eventually became Italic/ Venetian, the beginnings of the Romance branch of languages), Proto Iranian, Proto-Albanian, Indo-Aryan evolved into Vedic Sanskrit (precursor of Hindu), Proto- Balto-Slavic (the base of Russian/Czech/Hungarian/Slavic languages), Armenian, and the Proto-Celtic to Celtic languages like Gaulish, which evolved into Gaelic and Welsh and finally, Germanic languages, of which the earliest form written is Gothic (from the Goths) the root of English, German.
That's the biggest language group in the world, and it came from what we now call the Middle East, probably from somewhere between Iran and Russia. That's Caucasian Indo-Europeans, eventually.
So, this huge language group evolved very quickly because of the warring nature of the earliest of the Indo-Europeans, and it spread their language like wildfire throughout the Bronze Age world through conquest. Imagine how the Semitic tribes must have felt when this big and varied tribal warrior culture started steamrolling up to their boundaries?
I think the Semitic tribes (Proto-Babylonian/Chaldean, this is before the Hebrews branched off from the main Semitic tribes, Abraham's time) were able to keep their culture and languages from being assimilated by the earliest ancestors of the Assyrians and Hittites and other advancing Indo-European tribes simply because they were equally fiercely warlike, numerous enough, and had large walled cities for defense (such as Ur, where Abraham was from), and quickly adapted Bronze Age technology to their own advantage, weapons and armor, perhaps even also taming horses for warfare.
But, this "scrambling of languages" by the Semitic God Yahweh seems to reflect that some of the earlier Semtic tribes, proto-Hebrews, I guess you could call them, had succeeded in warding off the Indo-European invaders and their religions and culture, with their many new and strange languages and gods. It happened over many many hundreds or even thousands of years though...not in one year or even 10.
But, it was notable enough in the oral traditions of the Semitic tribes that it became part of their legends and the victory attributed, of course, eventually to their own "mighty" God of "armies", Yahweh, and eventually written down as part of the Hebrew Bible.
Anyway, that's my theory on how that folk tale came about, for what it's worth.