The crime committed by the Northern prison camp commanders were well known and condoned by the Lincoln administration and that includes Honest Abe his ownself. That would have been the logical destination for a proper investigation. As others posted in one way or another, the Union POW camps were much more political and ultimately sinister in their goals.
Compare any of those camps to Andersonville and you cannot find one instance where an offer was made to release prisoners unconditionally like President Davis did when the whole world knew about the travesty at Andersonville. He sent VP Stephens to personally ask Lincoln to accept a safe transfer of starving prisoners for humanitarian reasons, but it was too tempting for Honest Abe to make political use of all this cannon fodder. It is so bizarre that he is an icon for martyrdom when he singlehandedly made so many thousands of them.