If God gave us free will, any intervention on His part would contradict that. Performing miracles and answering prayers would bent people towards Good, which would undermine the idea of choice, and influence us towards Him.

So does free will exist? Because if it does, God is powerless to intervene or influence us by His own rules. Or does God influence us, and in doing so, removes our unbiased choice?

Perhaps this is why we call it a Mystery.