First, I'll start by saying that this topic is not about the anime. I'm aware that the GS Ball was dropped from the story because the writers wanted to fit Celebi into Movie 4 (although that doesn't explain why the GS Ball couldn't be carried over as well). While it is true that Masamitsu Hidaka confirmed that the ball was supposed to contain Celebi, that doesn't tell us much about the in-game event where Celebi did not come out of the ball. It's the same deal as Mewtwo being related to Team Rocket in the anime, but not in the games.
Those of you who have never watched the GS Ball sequence can do so here. In summary, the event took place after the the 16 badges had been collected, so the player had presumably even defeated Red by then. Kurt never got a chance to investigate the GS Ball since it started to shake while he was checking it. Following this, the Ilex Forest became restless, and this is what made the player aware that the GS Ball could be fit into the shrine. Then Celebi descended from the sky, and after the player either caught or defeated it, they failed to retrieve the GS Ball. What just happened there?
As I see it, Celebi did not want to see the GS Ball opened, so it distracted Kurt and the player; the only reason it appeared before the player was to make the GS Ball go through time so that no one would have access to it. This is quite feasible when you realize that in HGSS, Celebi encounters the player so as to complete the time loop whereby Ethan/Lyra prevents Giovanni from reuniting with Team Rocket. Clearly, Celebi is invested in the world around it and doesn't just go about its day guarding forests.
Now, whether or not the GS Ball is no longer canon on account of being replaced by the Giovanni event is immaterial. If you'd like, you can consider it as part of a parallel universe where Kris' journey took place; it is still interesting to consider what Game Freak had in mind ten years ago. What would have happened had the GS Ball been opened? What did it contain? One possibility is that it did contain Celebi from a future time period, and the one that showed up was upset by the realization that it would one day be trapped in a ball. Perhaps it did want to see the GS Ball opened and didn't think that Kurt could pull that off, so it sent the item forward in time.
But if true, the above theory would simply mean that Celebi was looking out for itself. Again, the Giovanni event essentially establishes Celebi as the only Pokémon other than the Lake trio that went out of its way to prevent a nefarious plan; Rayquaza merely reacted to seeing May/Brendan, and Giratina was protecting its own world. In light of this, I'd like to think that the Ilex Forest becoming restless was a symptom of Celebi being genuinely worried about something greater than itself. So what sort of danger could have surrounded the GS Ball? Hidenori Kusaka, the writer of Pokémon Special, interpreted it as someone (Pryce) gaining control of Celebi in order to go back through time; this was dangerous to everyone else because the void of time freezed everything near it. Obviously, Pryce was not designed to be a villain in the games, and the GS Ball wasn't created by Kurt, either. But it is possible that Kusaka had the right idea about the stakes involved. Could Celebi have been afraid of the Pokémon inside the ball?
Game Freak only expanded Pokémon-related stories from previous generations on three occasions: 1) Confirming that Mr. Fuji took Mew from Faraway Island, 2) giving the Regis a master said to have created them, and 3) linking Arceus to the Unown and thereby implying that the latter had a role in the creation of the Pokémon universe. Now, this also happened with Celebi in regard to the Spiky-eared Pichu and Giovanni events, but those events didn't reveal anything about Celebi itself that could help us understand the GS Ball. Plainly put, the GS Ball ended up being dropped from the games, too. Considering how late Celebi was distributed in Generation IV, it might just have been a matter of time constraints. It's certainly not unthinkable that Generation IV would have included another event Pokémon for an enhanced GS Ball event if Black and White hadn't been around the corner to introduce Victiny right off the bat.