This is not a true concept. It is not necessary in a Game of Chess to capture all the pieces of your opponent to win the game. It is only necessary to capture your opponents "KING". Now taking all of your opponenets pieces is one way to capture his King, but usually it is the most expensive way. In the game of chess in real warfare that expense is paid in Human Capital.
"Capture the king" was the game being played. Take out the Confederates Queen (the ANV and R.E.Lee) capture the King (Richmond and Jeff Davis) and the war would be over. The object of the federal war in the Trans Mississippi was to deny Richmond supplies coming from Mexico and Texas and from sending reenforcement east. Capturing the Mississippi R. and maintaining control of that barrier accomplished that objective.
In this game, Arkansas Post, was not a "target of oppertunity". In my opinion, it was a "target of Necessity". Whether McClernard and Grant and Sherman saw that and agreed or not is another matter. It posed a serious threat to Grants opperation against Vicksburg, which was the Key to control of the Mississippi. Arkansas Post was a direct threat to Grants Supply Line and had to be eliminated before it became too strong to attack effectively at the expendature of even more human capital.
"Did the federals occupy Arkansas Post and Ft. Hindman after they took them?"
No the federals did not feel the need for two bases on the Arkansas side of the Mississippi (i.e. Helena and Arkansas Post). Occuping Arkansas Post would serve no purpose to them and be another expendature of Union troops which they would need at Vicksburg. In Fact it was purposed several time to even abandon Helena and reestablish another base altogether at Napolean, Ar. being halfway between Memphis and Vicksburg to better protect Grants supply lines and the Chain the Arkansas River so the Federals would have to assign gunboats to watch for the adventures of the CSS Ponchartrain.
And don't worry about changing the nature of my post. Open discussion is always educational. And somebody will recieve the benefit of this threat. Maybe they will even become interested and in their research find the answer to my question. If someone knew the answer I feel that they would have already posted their thoughts. Part of the problem with Civil War research is that historians assign values to these kinds of operations. This battle is more important than that one, and this one effected more decisions that the others and therefore those which are concidered as "Lesser Battles" are not resaech as well as they should and it gives us a twisted understanding of what actual was happening.
I personally feel that in the game of Chess called "War" not all of the important moves are major battles, or even "battles" at all. That concept is what guides my study of the War in Southeast Arkansas, If I ever write a book it would be titled; "Nothing ever happened here, so nobody looked"