Why does Allah Almighty speak of Himself in the Qur’an in the third person (He is Allah), and not say (I am Allah), even though He is the Speaker?

What the questioner mentioned is iltifāt, which is a Quranic rhetorical device. It means shifting from one form of address—such as first-person (speaker), second-person (addressee), or third-person (absent)—to another, to embellish speech and diversify style. Speech becomes more eloquent when it shifts from one style to another, as this refreshes the listener's engagement and keeps them alert. As Allah Almighty said: "Indeed, I am Allah. There is no deity except Me, so worship Me and establish prayer for My remembrance" (Taha:14).