Is publishing any private fact a person wishes to hide "more than speech", or is it only publishing information about their genitals? I.e., what principle (if any) distinguishes between publishing a picture of Donald Trump's penis and publishing a (hypothetical) private racist conversation of his?
Well, we do have eavesdropping laws. You can record and publish a conversation as long as one party is aware of the recording. You need a wiretap warrant if you're a third party listening in. I don't think the same applies to photo/video, but I'm not sure how it differs if it does.