Taking the Mississippi River was an integral part of Gen. Winfield Scott's "Anaconda Plan" Which focused on choking off supplies, but the Mississippi was actually seen as a means to move troops more quickly into the southern heartland ... an offensive expedient for advancing Federal troops as much as a strategic cut-off against Confederate ones. The main focus was the blockade. He looked to starve the South into submission.

A lot of primary resources about that can be found in the official army records .... War of the Rebellion: a compilation of the official records of the Union and Confederate Armies.

Anytime an army can divide force concentrations and limit transport of personnel and resources, it is an effective way to wound the enemy (though Sherman's March to the Sea was a far more effective example of this strategic approach during the war ... and the Army of the Tennessee was only free to help Sherman after the fall of Vicksburg).

At the time, Gen. George McClellan had a similar outlook as yours ... and he may have been right. Regardless, lopping off the entire trans-Mississippi, strengthening the blockade (even marginally) and the symbolic aspect of sailing into the heart of the south, speaks for itself.