I would say the precedent is more to https://en.wikipedia.org/wiki/The_Night_Land - nothing about the Tower of Babel was meant to house anyone or be self-contained, it was merely a ladder to the heavens.
It's not canon, but in Ted Chiang's short story about the tower of Babel. The tower was perpetually in construction, so a whole society eventually flourished in the tower.
Some people never even left the tower because it took too long to get down from the place they were born.
Some people never even left the tower because it took too long to get down from the place they were born.