First, to deliver Israel from Babylon and second to make known to all the world the Lord's providence on behalf of His people. The idea of presenting a Gentile as an equivalent to a king of the Davidic line is an astounding one to an Israelite. The idea that the Lord would go outside of Israel to produce a king and deliverer for Israel seems to fly in the face of everything natural Israel has held dear regarding their natural lineage. It does, and the Lord points out to them that He will do as He sees fit in this passage. This passage also symbolically invokes the actions of the Lord as Creator, Judge, and Vindicator.
Victory pours down from above.
The purpose of the chiasm is to remind Israel of the Lev. 26 and Deut. The Lord's whole goal is to get Israel to be His people and He will use whatever means possible to do that in order to accomplish His purpose. If they rebel against Him to the point where the royal Davidic line is impeached, then He will use a Gentile king to accomplish His purpose. The Lord will not be thwarted in achieving the redemption of Israel, even if He has to go outside of Israel to do it.