I am doing no such thing as limiting the Christian Faith to the New Testament.
What I am doing, however, is establishing that the fullfillment of the Prophecy is the basis of the Faith.
All the pretext is exactly that- pretext. It builds up to, and boils down to “For God so loved the world, that He gave His only begotten Son...”
The actual event is what is important. (The Jews are still waiting for the Messiah- as per Old Testament prophecies... that come to a head in-and are put nicely in a nutshell into-... John 3:16.)
As you said, one cannot be without the other. But the result (the Message) is that God loves us! How much does He love us? John 3:16.
Now, if you want to get into “why” then that is far from my arguments. “Why” and “How” is addressed throughout the rest of the Bible. And yes, they are equally important. But- it is still the subtext for the fact that God gave His Son for us to live the Life Eternal.