Multiple Game Centre profiles for one Apple ID?

I have an iPad mini, my wife has iPhone 4S and iPad, my two kids have iPod Touches, and they all now are under the same Game Centre profile. It wasn't always this way, we each had our own Game Centre Profiles, so we could challenge, share games and still have one Apple ID to manage the purchases and signing up on all devices. Did Apple cut this out to make more money by having to have different Apple ID's per device to enable a different Game Centre profle? Or is there something I can do to get back to each of us having our own Game Centre Profle?

You can have multiple apple ids on a single device. I use my iPhone exclusively for 1 account and my iPad for multiple accounts.

Depending on the game, each profile has its own game save.

To log out if one profile and log in to another profile, go settings, Game Center, etc. I think you can figure out the rest.

With iOS 7, you can't log in and out from Game Center, which is kind of annoying.