To Game Center or Not

I’ve recently gotten the crazy idea of removing game center from my app.

I have made in-game leaderboards and a friend-system where people can add each other - i.e. a system that works on both Android and iOS. Game Center is currently integrated for iOS, with the same leaderboards as are already in the game.

I’m thinking that some (most?) users are actually annoyed by having to log into game center when opening the app the first time. And it seems kind of redundant to have it, given that I have in-game leaderboards and friend-system as well.

What benefits does Game Center have? Is the game in better standing with Apple if game center is implemented? Does one acquire many users through game center (not something I have seen yet). Would you remove game center if you were in my shoes?
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