Mirage isn't written badly per see. Her scenes are about showing her as a lonely character, that's why she barely interact with anyone. Episode 10 and 11 put even more emphasis on that.
Also, I don't think Mirage is going to be inspired by Hayate and/or Freyja. They aren't pushing her at all (like Hayate/Freyja did in the early episodes), they don't even seems to be trying to understand her actually.
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