Former Bungie composer Marty O'Donnell spoke with IGN in 2016 about the ending of Halo 2, which could explain why the game concluded on such a jarring and disappointing note.
“We just couldn't finish the plan, it was just impossible,” he said. “So, everything got re-jiggered, and we had the cliffhanger to end all cliffhangers.” The original ending, instead, had Master Chief and Arbiter “chasing the Prophet of Truth through the Ark and having a grand and glorious conclusion on Earth, finishing the fight right there.”
Of course, we'll never know what the Prophet of Truth face-off would've been like, or if it would've turned out as epic as it sounds. However, the ending that resulted in “the cliffhanger to end all cliffhangers” would've likely been an improvement over one that took three years to be resolved. Fortunately, however, the story can be played in full via Halo: The Master Chief Collection. Unlike gamers in 2004, you can see what happened in Halo 3 as soon as you finish the second chapter.