But I also have some specific reasoning that leads me to believe it's not a poor choice to provide another way to sign in. Signing in with facebook is extremely easy compared to normal signup paths. What this means is that most people who trust you with facebook will still sign in via facebook. And I don't think there's much of an argument that people who don't trust you with facebook will be signing in with facebook if it's the only option.
You can always allow them to link with facebook later, after they know what the game is, and after you've explained to them why linking will be valuable to them.