I have well over 100 PSA/SGC/GAI Auth cards and none list on the flip why its authentic.
I don't care though, I just realize its not good enough to warrant a numerical grade
and can figure out if its trimmed, recolored, skinned or what have you.
Here's a GAI card that I had SGC slab as well.
To me, it would be too "busy" if they added more info on the flip. I'm fine the way all 3 slabbers do it.
