Satan was a fallen angel?

Given that Isaiah explicitly states this is said about the king of Babylon, upon what exegetical basis do we have to saying that this is actually not talking about the king at all, but rather Satan?

”you will take up this taunt against the king of Babylon: “How the oppressor has ceased, the insolent fury ceased! “How you are fallen from heaven, O Day Star, son of Dawn! How you are cut down to the ground, you who laid the nations low! You said in your heart, ‘I will ascend to heaven; above the stars of God I will set my throne on high; I will sit on the mount of assembly in the far reaches of the north; I will ascend above the heights of the clouds; I will make myself like the Most High.’“ ‭‭Isaiah‬ ‭14‬:‭4‬, ‭12‬-‭14‬ ‭ESV‬‬

Wouldn’t it make sense that this is all said about a man? What’s the basis for believing it’s talking about some other being?