What Apple should do is turn GC into Social Center. Notifications, messages, widgets, game updates, and social components that give Apple users, Mac and iOS, a place where their social networks like Twitter, Facebook, and even Apple's own updates, can be located in one place.
It is possible?
I don't know if that's the direction Apple would ever consider taking but it does make sense to do this. Social Center would gather up iTunes, Messages, social networks, gaming and media into one place.
And what's more, the value of Social Center will only serve to augment other features and products that Apple wants to push out. As it stands now, I don't know how many people actually use Game Center but with Social Center, maybe more people will discover the value Game Center offers which could lead to more engagement and game sales.
Adding a component for music and other media sharing from friends and family could also lead to iTunes sales.
Apple should also add its own social layer that provides updates. Think of Path, a social network app, and you'll know what I'm talking about.
With Path, you can upload pictures, update status, sharing locations, and tell your friends what you're watching or listen to. Apple should adopt a similar approach (or buy Path outright). And Apple should be able to allow users to update that information to Facebook, Twitter, LinkedIn, Google+ or other social networks.
The bottom line is that Apple would then also have its own social network that could make sure it doesn't have to be at the mercy of competitors like Facebook or Google.
The question in people's mind is whether this could happen. Sadly, no. This is not in Apple's DNA. In all likelihood, Apple got stung by the failure of Ping and has sworn off social media services and apps. Game Center is as close as it'll ever come to that. To a lesser extent, iMessages is as social as Apple will get. Furthermore, Apple seems content to leave creating social apps and services to third party developers.
It's a shame. A native social layer would greatly enhance the values of not only Apple's hardware but its services like iTunes, iCloud, and future media pushes. Social Center would be the kind of next step achievements that Apple should be going after.