According to the Shaman King Wiki, Anna's Furyoku level at the start of the series was 3 times Yoh's at the end. She would have made a good addition to Yoh's team. Why did she not enter?
She herself claims that she is going to be the wife of the Shaman King, and that would not be possible if she entered, right? That reasoning would be typical for her. And I personally think that she's got a strong sense of what a woman must and mustn't do(even though I don't agree with her) and that also is why she didn't enter. Hope this is enough. :)