Am I the only one that's ever noticed that it looks like she's not just wearing heels but it's more like her feet ARE heels? At least, that's what it looks like to me. Like it's just a part of her body. It's pretty weird.
I imagine for the same reason the little magical AI is wearing anything at all, stylized to look like a presentable servant to a goddess or would be hero I imagine. No one likes a naked program spouting their wiki advice.
I go with the feet are heels idea from above as well. That might tie into her gracefulness, especially when she performs dances at several points of the game and basically skates around the air