Storm taking command is not a major plot point. It could have been eliminated from the script entirely and it would not affect the Cure or Phoenix storylines.
But these are ensemble movies. The X-
MEN. And thus the supporting characters should be present and have interaction/conversation about the major plots. Otherwise, why not just make a Wolverine & The Phoenix movie?
Even with this plot point in the film, there is no reason, from a story perspective, that Storm needs to be developed in order to take command of the school. Storm could be an entirely silent character in the film, standing in the background, and she could still take command of the school with a simple line of dialogue:
Beast- "Storm has taken over the school"
Yes, that is extreme but I'm trying to illustrate that Storm's actions are not important from a story perspective. Her little weather scene, Eulogy, battles with Callisto, and minor interactions with other characters can all be eliminated from the screenplay without much (or any) effect. That is the mark of a minor, unimportant character and evidence that the screenplay was weak in devoting screentime to her when it could be better used developing the major characters in the story.
Events in the film - the emergence of Jean/Phoenix and then her departure (from the team/mansion) - are going to have an impact on the supporting characters. Even without the exit/death of Cyclops and the death of Xavier, it would have necessitated the only other senior person in the mansion (Storm) to be given some time to be shown reacting and taking action. As someone who worked with - and lived alongside - Jean, it's natural to show Storm having a presence in the story. Whatever dramatic actions were carried out by Phoenix - and they would be dramatic in any script written that featured Phoenix - would mean Storm's point of view and responsibilties would be part of it.
You seem to be advocating the absence of Storm altogether. How would that have taken place, given that she was part of the previous films (not to mention a popular comic book character). There's no logical way that Storm could be written out of the third film entirely.
Now, as for the character moments you didn't like in X3, we had similar scenes in X2 - such as Iceman's coming out scene with his parents - that serve no purpose to the main plots (which, again, relate to Wolverine and Jean). And the scene with Jean, Storm and Nightcrawler in the church has a lot of extraneous material that's not significant to the plot. But it's there because it adds characterisation and backstory.
The conversation between Storm and Nightcrawler on the jet is another example of a character moment that doesn't serve the plot, but there was nothing wrong with it. Similarly, the scene where Mystique goes into Wolverine's tent in disguise, and where Mystique and Nightcrawler have a conversation, don't contribute anything to the plot. But those moments matter - and they matter more for the supporting characters.
In fact, the Storm/Nightcrawler conversation, in which she reveals they are sheltering at a school "where we can be safe... from everyone else" is followed up on in X3 when Storm asks Xavier why they are still hiding at the mansion at a time when they have a more understanding president and a Dept of Mutant Affairs run by Beast. So the X3 scene isn't some random addition.
I would say also that Jean/Famke had a good amount of characterisation and screentime in X3, except for when she was stood around at Alcatraz. And we saw that Wolverine spent the entire movie preoccupied with Jean.
The elevation of the Cure to the main plot has been claimed to be a studio decision, so the writers should have linked it to the Phoenix plot by having the cure development fast-tracked as a result of the threat/destruction caused by Phoenix. Even then, it's hard to see what Wolverine's standpoint would be because he never seems to have any view on wider issues like the Cure. He wouldn't want it used on Jean, though; or maybe he would, if it meant she would be back to normal.
In the end, I certainly don't think Storm dominated the movie. Some of her scenes could have been better written/executed but I don't think she took screentime from anyone and it certainly wasn't down to Storm that Jean stood around on Alcatraz. They should have had the two of them take to the skies in an elemental battle of the goddesses, in which Storm eventually used hurricane winds to blast Phoenix miles out of the way for a time before Phoenix returned for the Alcatraz destruction scenes we did see.
If what you are saying amounts to a dislike of Storm, that's the fault of the films for not giving us a better Storm. If what you are saying amounts to a criticism of Storm's portrayal, the most of us agree.