There’s also the suggestion that, since the Mesopotamians continues speaking Sumerian (until conquered by Akkad and Sumerian became the Mesopotamian Latin) and they carried on building Ziggurats until Assyria, wouldn’t that, rather than Babel, explain any resemblances without proving the Babel event?

Sumer is most likely the land of Shinar in Gen 10:10, which is where the tower of Babel was located. So, the tower of Babel and the Sumerians had a close relationship.

Gen 10:10 (ESV)
The beginning of his kingdom was Babel, Erech, Accad, and Calneh, in the land of Shinar.

The discovery of Sumer was, more or less, an accident. The archaeologists and scholars Kramer refers to were drawn to Mesopotamia in search of biblical correlations. The Bible made cities like Babylon and Nineveh infamous, and so the Babylonians and Assyrians were well known to 19th century scholars. They began their excavations in Mesopotamia in an attempt to confirm the historicity of biblical stories such as The Great Flood or the Tower of Babel. The only reference to Sumer in the Bible is to `the Land of Shinar’ (Genesis 10:10 and elsewhere), which people interpreted to most likely mean the land surrounding Babylon, until the Assyriologist Jules Oppert (1825-1905 CE) identified the biblical reference with the region of southern Mesopotamia known as Sumer and, further, asserted that cuneiform writing was Sumerian in origin. … he-future/

Sumerians likewise had a global flood myth.

Thus it was established that long before Genesis was committed to writing, the ancient Mesopotamians had themselves told the story of a universal flood sent by divine decree to destroy humanity. Soon other texts were discovered that gave similar accounts in several different languages – Sumerian, Old Akkadian, Babylonian – and in several different versions. In the oldest, found on a tablet from the city of Nippur, dated to around 1800 BCE and written in Sumerian, Noah’s role is taken by a King of Shuruppak called Ziudsura or Ziusudra, meaning `he Saw Life”, because he was awarded immortality by the gods. In another, written in the 1600s BCE in the Akkadian language, the protagonist is called Atrahasis, meaning `Extremely Wise’. (69) … he-future/

“There has also been speculation that the ziggurats were used by ruling class during flooding as a safe high point.” … -pyramids/

Even if one accepted anything but the limits of building tall structures dictating piled up mountains or stepped structures. The existence of ziggurats and pyramids explain the similar structures elsewhere without being any evidence for a tower of Babel.

I’m not claiming ziggurat-like structures all over the world is conclusive evidence that they all share the same origin. But, it is an interesting coincidence that we see these structures all over the world and one of the earliest, if not the earliest, is described in the Bible.