Game Center as it is at its present state is a badly implemented good idea. I've had lots of achievements that did not sync when earned offline, you can't send messages to your friends etc. Apple need to work on their priorities since the main sell of their devices is gaming. They could have layed out a structure for gamers, but I think it also has to do with game devs who aren't willing to spend time on coding and such.
Imo, Apple needs to completely redesign and redefine Game Center like what they're doing to iPhoto on OS X Yosemite.
But Apple has bigger priorities now.