I wouldn't say so. To say that Zazu is a "worthless character" is going a little overboard.
Although he is my least favorite TLK film character, I don't disrespect him which is the wrong thing to do. Just like all the other ones, he serves a purpose in the films as well. And so this is something to consider firsthand.
It kind of goes back to Timon being a non-lion character as well but has a bigger role in the films than Zazu, and also being the central main protagonist of TLK 3.
But in my opinion about himself, I don't see how Zazu served much comic relief to this TLK film when even Scar and the other main main characters had some of their own too in the movie.
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On a side note and based on what was written by the topic poster, "The Lion King" is simply the title of this and its following two film works. It's used to identify this work out there and it doesn't determine that that is what the films are actually about.
It goes with basically every film out there that is truly good. But then again, each and every film is its own work, despite if its also part of a franchise.