[FWIW, in the books, Oz is a real place, and not just a dream of Dorothy’s per the movie. I’m going with the books. If Oz is a dream of Dorothy’s, then Glinda has no independent existence or motivation to discuss.]
I feel there are a few holes in Pepper Mill’s version.
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If Glinda sees Dorothy as a threat, why doesn’t she just send Dorothy home right away? If that happens, Glinda’s in better shape than she’s been, since Oz is minus the Wicked Witch of the East. And since Dorothy is so clearly clueless, once she’s gone, she’s not coming back again. What Glinda wouldn’t want is for her to stick around and figure out whether she’s got any powers.
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“I feel that Glinda knows that the Wizard is a fake and can’t do anything himself about the Wicked Witch. After all, if he could have gotten rid of her, he would have done so soon after he got to Oz.” OK, but if the Wicked Witches of the East and West are sisters and presumably allies against Oz, Glinda, and whoever the fourth witch is, it’s quite possible that if the Wizard were a real Wizard, he might have the power to take on one Wicked Witch but not both at once.
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If Glinda believes the Wizard is a fraud, how is he a meaningful rival? She’s got magic; he doesn’t.
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Unless she really thinks Dorothy has some extraordinary powers, why does she think sending Dorothy anywhere will accomplish anything but killing off Dorothy? Why not dispose of her kindly by sending her back to Kansas right away?
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If she does believe Dorothy has some extraordinary powers, see (1). You don’t want your rival to find out what she’s capable of.
Either way, ISTM that it’s a real long shot that Glinda’s going to come out on top as a result of sending Dorothy to the Emerald City. She’s already ahead in the game because the Witch of the East is dead. Why not send Dorothy home, and see how the new balance of power shapes up?