Your explanation does not satisfy me for one reason- it’s not concise.
The question at hand is “Why did God send Jesus?”
Your response is “to bring us all back into His family.”
Mine is “He loves me.”
Sure, since He loves me, He wants what you state- but your explanation is so sterile. So exclusive.
God loves me. And His Grace is sufficient for me. From there, we learn to listen to His Wisdom. Therefore, because of the relationship started (and proved) by His Sacrifice, the rest of His message NOW has meaning.
If He did not love us so, then the rest would be unimportant and of no consequence.
If you are familiar with computers, you might refer to this as the system’s Boot sequence. Without this code, the rest is useless flop. Software with no way to be understood. Not in any manner it’s MEANT to be understood, anyway.
This is where we part company. I see God's plan made known in the story of creation and our redemption first announced with the protoevangelium right after our fall... you see our relationship with Him started with Christ on the Cross. It's a matter of perspective.
Good night.
BTW, I see it more as the systems reboot sequence.