I think maybe JKR knew that if she replied it would get more attention. She is a very clever woman.
But I think she also knew that every time TRAs pull a stunt like this doxxing they get bolder. If she didn’t put a stop to it, it would escalate.
Maybe she also wanted to make an example of these TRA doxxers. She has the legal resources to drag them through the courts and sue them to hell and back.
She mentioned other less fortunate women in her post. They don’t have those resources but would benefit from a court case showing how unacceptable this is.