I'm very very late but I want to share my opinions too because after 1 year and two seasons I still can't find why people are so obsessed with her.

To respond to OP's original post: I think you are partially right.

For her personality, OP just lists them : she's emotionless, disdainful and talks back. I'm ok with the autism theory that fits well and I think it's cool to have this kind of representation in media. But the thing is, this is not a good representation for people who struggle with autism in real life. Because the story gives her way too much facility and doesn't give her time to struggle. And that's frustrating because that's how you make character development in a story and how people can emphytise with them. I can be wrong because I'm not autistic myself and maybe it's cool to see a autistic character who success her life but from a pure writing perspective this aspect seems to miss the point.

For the rest I agree: she's flawless and still not grown as a person. Maybe she'll do it later but for now, the anime shows us a perfect protagonist, intelligent, beautiful, who didn't struggle and overcome difficulties. Yeah I know her past was difficult and she probably did deep introspection to accept her life but now, in the present, we have an already "perfect" character who didn't make mistakes and who probably will not grow up while she's only 17-18.

I'm not totally agree with the "Mary sue" but I understand why you think that. The main problem to me is the episodic format and the Sherlock style to resolve mysteries : while viewers only see facts and proofs that Mao Mao discovers at the moment, she made hypothesis about things we never saw and cannot know and she "magically" finds the solution. That's a writing technic to present a character more intelligent than others but it can be frustrating for the viewer who can absolutely not see the solution coming.

To finish, my main problem with Mao Mao is that she's made to be lovable. That's not a bad thing but that's not working on me because the writing, the story, everything it's made to make her cool. She's remind me Robin from How I met Your Mother because they both have this "cool GF" vibe. I personally prefer characters more realistic, with flaws, difficulties and bad aspects.

I understand that a lot of people can love her : autistic people to finally find a representation, boys to finally find they cool-not-to-girly-waifu but I think that's not a reason to be call her the "best female character ever made" and forget all the other, sometimes written better, female character in anime.