Perhaps your question is answered by the lack of responses: not a common or widespread problem.
The part(s) in question are the applique. They are replaceable and about $40-$50 each online. Replacement looks like a mildly difficult task and may lead to replacement of weatherstripping if necessary.
I did a search for this and found a bunch of posts of the black applique peeling in the Impala forums. Only fix is replacement or living with it. We just haven't seen much here as the early gen9s are now just closing in on 4-5 years old.