With ChatGPT, this can be extended to create emails that look very personal - as if someone has followed all of your work and is genuinely interested in what you are up to - with extremely low effort. And people are already doing this, I already get emails like this today.
Should emails be private? I don't know - I personally consider them to be public because I know for a fact mine will eventually be public whether I like it or not. But I am aware AI is out their slurping up every public communication I've ever had, and is likely trying to manipulate me in various ways already today.