I happen to be a 34 year-old fan of Idina. I recognized her talent when I saw her in Rent a month after it won the Tony. There was no CD at the time and I'd never heard of her, but she gave one of the most memorable performances I'd ever seen.
And I completely agree with enjoying_broadway. There is no ONE technique that applies to all singers and voices. I don't find Idina's belt shrill or creamlike in the least. The "shrill" sound is the natural quality of her voice which cannot be changed without major surgery, very much like the heavily lauded voice of Kristin Chenoweth. Kristin has stylized her voice more heavily to use to her advantage for comedic roles. Idina is a different "type", so her voice is less stylized, but essentially, they have remarkably similar voices. Kristin uses more of a head mix, while Idina uses more of a chest mix.
As for screaming, that implies vocal fry which is not evident in the Tony performance or on the Wicked CD. She uses a little bit of it in Rent for the purpose of musical style, but not in such a way that would be harmful or damaging to her voice. If she were screaming, she would have missed half her performances from burned out vocal chords and exhausted throat muscles.
"What can you expect from a bunch of seitan worshippers?" - Reginald Tresilian