Wow there are some far reaching theories out there, yet nobody has bothered to cover the most basic theory of them all. What about the fact that 'The Real One' just wanted to protect Yahiko's body?

He could still have some sentimental connection to Yahiko, especially if the one controlling the bodies is Nagato. OR 'Real One' knows that God Realm is the strongest, and his invasion would fail without it's powers and ability.

I'm not saying that God Realm isn't the key to defeating Pein. I'm saying that I believe either the real Pein simply protected his strongest weapon, or Nagato protected Yahiko's body, or probably both.