Chapter 11

[georgiedenbro]

You can't be a female KH. It's in the very definition.

Well it all depends on your definition. So long as we consider a KH to be just a male BG, then no, you're right. But it seems what the male KH could do was to access both past and future lives, including presumably the male ones. And it seems Alia could do this. The BG didn't know this is what the KH would be able to do, possibly because, being women, they didn't understand prescience very well. Paul was the KH, but not at all what they expected. And Alia could do what Paul could do, so despite it going against the current BG assumptions, she was essentially a female KH. Now it's a fair question to ask why she had prescience at all, since neither Jessica nor Leto (as far as we know) were prescient.

[Cpt. Aramsham]

"Because the memory of being human is so rich in him. Think of all those lives, cousin. No.
You can't imagine what that is because you've no experience of it. But I know. I can imagine his
pain. He gives more than anyone ever gave before. Our father walked into the desert trying to
escape it. Alia became Abomination in fear of it. Our grandmother has only the blurred infancy of
this condition, yet must use every Bene Gesserit wile to live with it -- which is what Reverend
Mother training amounts to anyway. But Leto! He's all alone, never to be duplicated."
~Children of Dune

That is a good quote for your position, but I don't think it is very conclusive. We can take Ghanima to refer to the experience of having memories of many lives in general, not necessarily ancestral memories. So for Paul it is the memories of uncounted possible lifetimes experienced presciently, and for Jessica, the "blurred infancy" of the condition means the shared memories from other Reverend Mothers, just like Leto referred to earlier in the book.

Spoiler for Heretics/Chapterhouse:

It would also apply to the Duncan of the last two books, and there it is clear that the experience of his many ghola lifetimes has granted him Kwisatz Haderach-like powers.

Otherwise, to claim that Paul went into the desert to escape ancestral memories rather than prescience seems to me like a massive retcon.