I don't understand, why is that a bad thing? Maybe it might be an issue if you're trying to do something anonymously (but at that point, you shouldn't be using your regular machine anyway).
"Privacy: a secret matter."
"Privacy: freedom from unauthorized intrusion."
"Privacy: the quality or state of being apart from company or observation."
So you see, privacy IS security.
Not just any public key, it's your public key. It identifies you.