Harry Potter and the Goblet of Fire cut the full performance of the Hogwarts School Song, but why? J.K. Rowling's magical novels were brought to the big screen in the early 2000s and quickly grew in popularity. After the release of three Harry Potter films between 2001 and 2004, Harry Potter and the Goblet of Fire hit theaters in 2005. The movie focused on the Triwizard Tournament that Hogwarts was hosting and saw other wizarding schools compete against them in a series of challenges.
The tournament allowed the franchise to introduce two of the other biggest wizarding world schools, the Durmstrang Institute from Eastern Europe and the Beauxbatons Academy of Magic from France. Once the school members arrive at Hogwarts, Goblet of Fire introduces them to viewers and Hogwarts' students in style. The boys of Durmstrange Institute chant, run, and leap through The Great Hall, while the ladies of Beauxbatons charm and dance through the isle with Madame Maxime walking behind them. Despite these introductions for the other schools, Hogwarts didn't receive one - even though it was filmed.
One of the deleted scenes from Harry Potter and the Goblet of Fire shows the students of Hogwarts showing their school spirit right after these introductions. Harry Potter, Ron Weasley, Hermoine Granger, and the rest of the school's students and teachers begin singing the Hogwarts School Song, which is a short anthem about the greatness of the school. Even though the scene was filmed, it was not included in the final cut of Goblet of Fire, and it is easy to understand why: it wasn't necessary for the film or franchise at this point.
By the time Harry Potter and the Goblet of Fire hit theaters, audiences had already spent several years and films with the students of Hogwarts. As a result, the song doesn't provide viewers with anything new, while the songs/performances from Durmstrange Institue and Beauxbatons Academy of Magic help introduce them. These numbers show general audiences how the new schools are different from Hogwarts. The song also, clearly, could be removed since it had no effect on the plot and was more just an opportunity for Hogwarts to get a moment of its own.
Even though the Hogwarts School Song is a part of the books, it only appeared in the first novel and not in Goblet of Fire. However, the movie did still include a portion of the song into it, as Harry, Ron, and Hermoine sing it briefly earlier in the film. If that snippet of the Hogwarts anthem wasn't enough, the good news is that the alternate plan for the song can be found in Goblet of Fire's deleted scenes. But the scene is also sometimes added to re-runs of Harry Potter and the Goblet of Fire on cable so fans can see the scene in its proper context.