I think a lot of her S ness comes from her culture. She was well brought up and wanted desperately to fulfill what she was told were her roles, but she kept being thwarted one way or another from being a happy wife and mother, sorority sister, pretty girl without a care in the world/let the men do the heavy lifting, etc. It's why she always shows up on the feminist poet list. I don't think she was all that mentally ill. I think she was extremely bright and perceptive and could see what she was not supposed to see -- and developed a habit of examining what she was not supposed to look at -- and that made her unadaptive. I feel like it's possible if she were young now, she wouldn't be considered crazy.
P.S. I think she's a T. Very intellectually competitive. And between hers and Annwn's poems, above, I prefer Annwn's. Sylvia's is so contrived. There's so much device going on. You can see the work.