The most important parts of Chamberlain's memoir, and the point of honoring the actual fighting men of the Confederacy (monuments/statues/etc.) are this:
"Bayonets were affixed to muskets, arms stacked, and cartridge boxes unslung and hung upon the stacks. Then, slowly and with a reluctance that was appealingly pathetic, the torn and tattered battleflags were either leaned against the stacks or laid upon the ground. The emotion of the conquered soldiery was really sad to witness. Some of the men who had carried and followed those ragged standards through the four long years of strife, rushed, regardless of all discipline, from the ranks, bent about their old flags, and pressed them to their lips with burning tears.
"And it can well be imagined, too, that there was no lack of emotion on our side, but the Union men were held steady in their lines, without the least show of demonstration by word or by motion. There was, though, a twitching of the muscles of their faces, and, be it said, their battle-bronzed cheeks were not altogether dry. Our men felt the import of the occasion, and realized fully how they would have been affected if defeat and surrender had been their lot after such a fearful struggle.
And the part about them co-mingling and becoming countrymen again.
You can't strip Southerners of their heritage and expect them to continue to have a sense of belonging to the U.S. It's done deliberately, SPECIFICALLY to invite discord and a desire to break up the Union, AGAIN.