I agree. Furthermore, I have to add a little piece to your puzzle...
The Sage didn't just give some information to the Elder Son through the Tablet. He told the Elder son that Peace couldn't be achieved with power alone, and the proof is the history of how Kaguya Ootsutsuki failed to reach peace using power. In other words, the Sage gave the Elder son the proof of why 'power' alone wouldn't work, he changed Madara's insight about peace.
The Sage didn't just give some information to the Elder Son through the Tablet. He told the Elder son that Peace couldn't be achieved with power alone, and the proof is the history of how Kaguya Ootsutsuki failed to reach peace using power. In other words, the Sage gave the Elder son the proof of why 'power' alone wouldn't work, he changed Madara's insight about peace.