The first sentence is a non-sequitur. But, I disagree. It does rightfully sets up the LOTR. FWIW, I have read both the Hobbit and all of the LOTR. They fit well together.
If you take a look at Star Wars, just one example I am pointing out here, you can tell that most people are not a fan of prequels. So with a story, usually you should go forward with it. What happens next? Instead of going back. Most of the time, it doesn’t work very well. Just my two cents.