Most of these battlefield memorials (like at Gettysburg, Shiloh, etc) had unit memorials placed within a 20-year period after the war. Some of these were sponsored or paid via the officers surviving the battle. Lot of examples at Gettysburg.
After the war, it became like a religious experience for some members to return and talk about the 3-day battle. This led to battle-tourism in the Gettysburg area, and a number of hotels were built as part of the landscape.
My point here is there are two eras for the memorials/statues. This 1900s era became a magnet for the Democrat Party in the south, and you can find local statues all over Georgia, SC, Alabama, Miss....that came in this wave of renewed enthusiasm for the war. All of this helped in getting Wilson elected in 1913, and bringing in 67-percent of the House seats to be Democrat.
The National WWII Memorial was dedicated May 2004. Do you know why?