Unless I am misunderstanding you, to be fair, plenty of Christians do claim that. They claim Jesus is god (and the holy spirit is god for that matter), and that the bible is the divinely inspired work of god. Therefore, the bible is the divinely inspired work of Jesus. Also, I am pretty sure there is a large subset of Christians who would take exception to your "Jesus isn't even in the bible until the new testament" argument and would state that the entirety of the bible is about Jesus. In fact, i believe I saw a pretty well known npub on her state that just the other day. If you are saying that only the words of Jesus matter in the bible, then why revere the bible at all...if you don't take the entirety of the bible as a whole being the divinely inspired work of god, then what is your justification for following Jesus?