I reported my experience with the AI elsewhere in this forum. In brief, the AI does not attack my armies. It goes after small groups, up to about three units. But there is no Shiloh, or Gettysburg, or Stone's River, etc. At the same time, unlike real life, not fighting the enemy armies does not seem to hurt National Morale.
I think it should. Not fighting probably hurt the Union as much as, if not more than, the defeats. I would like to see the AI fight other major forces, suffer a penalty if it does not, but benefit in some way even from defeats. One benefit could be that, without fighting, National Morale goes down more than with a defeat. Another would be that soldiers and generals could get valuable experience and improve from defeats as well as victories. I believe that right now defeats reduce experience. This should be reversed. Every time Lee gave the AoP a drubbing, he was training the Union army to get better. These are the only ideas I could come up with, but perhaps others will chime in with better ideas.