I could not think of any reason for adding a binding like you mentioned so....I searched and watched a youtube about "Chunky Binding" and it is a design feature that turns the binding into more of a wider frame around the quilt. This presenter explained why she might leave the batting longer but it is only when the chunky binding might impact the pattern on the front of the quilt. In the demonstration she used a traditional well squared up quilt sandwich and moved the binding about one inch in on the quilt. Sound confusing? Here is the link to what I watched.
https://www.youtube.com/watch?v=lea_zNEXu5s
I might try this if it would enhance the quilt and not detract. It could be an interesting addition.