The sixteenth trump has had more names than any other card, and none of them is Babel.
The French title is La Maison Dieu, the house of God, which in period usage most often meant a hospital or almshouse rather than a temple. Italian decks call it La Sagitta or Il Fuoco, the arrow or the fire; other variants give La Torre, the tower, and some early lists name it Il Fulmine, the lightning. The card is also absent, along with the Devil, from the surviving Visconti-Sforza material, so we cannot say what the oldest complete tarot did with it.
That spread of names matters because it shows the card was not understood as one thing. A tower struck by lightning, a house of charity destroyed, an arrow from heaven and a fire are related images but they are not identical, and different cities were evidently reading the picture differently. The identification with the Tower of Babel, which most modern books offer as the card's origin, is a later rationalisation. It fits the image; it is not attested as the source.
The Golden Dawn assigned the card the letter Peh, the planet Mars, and the twenty-seventh path from Netzach to Hod, the horizontal path low on the Tree, which in that system is the one that breaks a false equilibrium. Peh means a mouth. Crowley made this the most violent card in his deck and read it as the destruction of the ego's house, which is a Thelemic reading and not a general one.
The falling figures, the crown knocked askew and the raining points of light are stable across most versions, and they are the part of the image that has always done the work.