You already have this for members profile pages - why not add it for GROUPS as well??? Prior to switching to Inspirebook we achieved this with using Brajesh (BuddyDev) plugin which we managed to adapt to allow BP groups to change/upload a cover image, we also allowed groups to choose their own bg image to the page or color - WHAT we DID notice is that we had an immediate increase in people wanting to register groups and style their group pages (yep even in FB it was a holy grail)…
In my opinion you already HAVE this for member profiles, just add it to group profiles??