That Britney gif is amazing!
There were actually moments in X2 when Storm could fly (when the team enter the base we see a bit of wind and soldiers looking confused) but for reasons (probably budget) that didn't happen. Storm did have two big 'saving the day' moments in X2 but all Halle had to do was stare and let the VFX do the rest in post. Storm never had an arc or storyline in Singer's film, she was just there, and I can't imagine what Storm would have done if Halle's profile wasn't raised between X1 and X2.
I also heard from X2's DVD commentary that Storm was supposed to stop the policemen during the raid on Bobby's house instead of Rogue touching Pyro's feet and using Iceman's power. But once again, it was too expensive for them to do that.