Carol also lost her memories due to Rogue stealing her powers. Professor X managed to restore them but she doesn't have any emotional connection to her memories. She spent some time as the X-Men's pilot and intelligence operative. Due to the experimentation of the Brood, the full potential of her powers were unlocked and she became Binary. After touring with the Starjammers, she lost her Binary powers but her Ms. Marvels were fully restored.
Blunt would be good for the role. I just think there are a few better choices before her.
For me, Chris Claremont's Ms. Marvel stories in the X-Men were much better than all her solo comics.