The case isn't about morals of "journalists", or investigators, even. It's about evidence, so far which seems to be lacking.
The problem with attempting to legislate against currently legal, but potentially immoral, tactics, is that it takes away from a free press. While you might try to say that there is no public interest in certain parts of the case (eg Zachary's birth certificate), but for other parts, there is a legitimate public interest. You are also talking about people who regularly throw themselves at cameras, and go to a lot of loose lipped parties. If you stop this kind of reporting or investigative journalism, you end up putting too many people behind a wall of privacy (eg politicians, if we want to get particularly topical).
A free press is an essential part of our democracy.