I think they were pretty clear about it. There is nothing PHYSICALLY wrong with her. It seems to be that the new mind reading powers are just making it difficult for her to communicate. It isn't that she physically can't speak, it's more an issue with her awareness and having a proper divide between whats physically spoken and what's just going on in their heads.
so, no, she can't write.
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"I can do it if I try you know! It’s just that I don’t try, but I could do it if I did try! I think?" - Shiro
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