Well, apparently she wanted to, but was under contract with Disney to do "Princess Diaries 2" at the time instead. Tis unfortunate... but then again, if she had played Christine, we might not have gotten her as Fantine 8 years later (and the POTO movie might've ended up hurting her career due to Schumacher's general ineptitude). I think she and Hugh Jackman both dodged a bullet by not being in that film, really, though they would have undoubtedly been better than the people that were chosen.
And Ramin Karimloo hadn't played the Phantom onstage by that point (and was several years younger than Gerard Butler or Patrick Wilson), so I can kinda forgive them for not having him play the Phantom. Though he should have at least gotten to play Raoul. Then again, if he'd gotten a bigger role, it might have hurt his career too... so perhaps everything worked out for the best (especially since he got to play the Phantom in a far better filmed version of the musical later on).