delete
No, I wouldn’t do this. Like you said, all women experience sexism (or at least, the vast majority will have some example to offer). If you wanted to make this a personal statement, that would be one thing, but it’s not a diversity statement. Also, if you do decide to write this for a personal statement, I’d be very careful in how you handle “you’re too beautiful to be taken seriously!” - it’s obviously a sexist comment but it can read as though you wanted to work in a compliment on your looks.
I wrote a diversity statement about sexism as a woman in engineering. It’s hard to tell how any part of your app hurts or helps, but I got into every school I applied to except Stanford, so it can’t have hurt too much.
As long as your diversity statement is well written I don’t think it will hurt.
If you’re writing about a specific context where women are demonstrably underrepresented, that’s one thing. I didn’t get that impression from the OP, but I could be wrong of course.
One could argue that “most all” of any under represented group experiences a type of -ism. It’s your story and how it made you the person you are today.