In the time the tower was constructed, it could have only have been as tall as the smaller skyscrapers of today. So why has god not destroyed these?
Because the Tower of Babel was a religious object designed to reach to God. Height isn't the point, motive is. The same idea continued in many human-originated religions, and is still shown in the Mayan and Aztec ruins of places where they performed human sacrifice to the gods. Modern skyscrapers don't have a religious motive.
Why would god even be threatened by this "tower"? He hasn't appeared threatened by our towers.
Never occurs to anyone that God did this and many other things for the protection of humanity, does it? By scattering the people away from Babel God kept them from developing a powerfully evil religious system that would only put humanity on a par with the fallen angels. That's also why He closed Eden to them and put the flaming swords to guard the Tree of Life, lest they take of it and live forever the way the devils do, destined only for eternal suffering. He hoped to preserve humanity and eventually save many from such a fate.