Yes, the real reason for the vanishing of the Moabites, Ammonites and Philistines is that God’s judgment was against them. To his prophet Ezekiel, Jehovah declared:

therefore I will clear the shoulder of Moab totally of its cities, the jewels of the land: Beth-jesimoth, Baal-meon, and Kiriathaim.

There is overwhelming evidence that this prophecy was fulfilled. Ammon and Moab did indeed become the “possession of the Easterners.” Says archaeologist G. M. Landes:

“Archaeological explorations have shown that sedentary occupation in the land of Ammon virtually ceased before the middle of the 6th century B.C. . . . Into the vacuum created by the destructive advances of the Babylonians poured once again . . . the ‘sons of the East,’ the bedouin hordes from the desert, who now destroyed all formally organized political activity in this area, and brought to an end the semi-autonomous Ammonite state.”​—The Biblical Archaeologist Reader, Vol. II, pp. 87, 88.

Regarding Moab, scholar A. H. Van Zyl writes:

“The fate of Moab was severe. When the power of the state had once been broken by the Babylonians, the children of the east could encroach upon the cultivated land, for the former inhabitants of the line of fortresses, who had so boldly defended their country during the past centuries, had been abducted. The only service that these fortresses and the pottery remains in their vicinity still render is to tell the story of the downfall of the Moabite Kingdom and civilization in the first quarter of the 6th century B.C. After this depopulation of the country, we still have some references to individuals of Moabite origin, but there can be no reference to the Moabite nation or state after the first 2 decades of the 6th century B.C.”​—The Moabites, pp. 157, 158.