The tower was built to watch people, not touch the sky
The builders of the tower sought not merely height but surveillance: a structure tall enough to let appointed overseers watch the whole surrounding settlement, so that no one could slip away to another land. Their deeper fear was ideological rather than geographic — since people's minds naturally differ, they dreaded that dispersal would lead to divergent beliefs, and so they enforced uniformity of thought by force, even to the point of executing dissenters, as was done to Avraham. The "tower" thus represents a regime of coerced conformity, not simply a architectural ambition.AI summary · anthropic/claude-sonnet-5
“And they said, “Come, let us build us a city, and a tower with its top in the sky, to make a name for ourselves; else we shall be scattered all over the world.””
And its top in the sky - It is obvious that you should not think that this would be one city to the whole world, rather they thought that the other nearby cities would be subjects to that city that had the tower, that they would be able to see from it to the distance, over all their settlement, so that no one would be able to separate themselves and go to another land. That's why they needed its top reaching the sky.
And we will make a name for ourselves - people were set up to watch and be in charge of the thing, and they were army chiefs in charge of punishing those who would cross, since if this is not the case there would be no need for the tower. And all that was due to fear/suspicion.
Lest we be scattered over all the face of the earth - However, we must understand why they feared that someone might leave to another land. And it is understood that this was related to the uniformity that was among them. And since the opinions of people are not identical, they feared that people might abandon this philosophy and adopt another. Therefore they sought to ensure that no one would leave their society. And one who veered from this uniformity among them was judged with burning, just as they did to our forefather Abraham. And the "same words" can also be seen as the fact that they would kill whoever did not think like them. And more is explained on verse 6.