I'm afraid I don't understand your point, ab.
The press should obey laws, just like anybody else, but they're not. That's the point. They often get away with what they do, because most people don't have the finances to take them on.
Section 40 isn't about state regulation. It's about setting up a system, which newspapers can choose to opt into and limits their liability.
In a democracy, it's essential that we have not only a free press, but an honest and responsible one. Personally, I don't think we have. Failing that, people need to be more cynical about what they read. Compulsory media studies?
The other part of the petition is about Leveson Part 2, which will probably not happen anyway. It's specifically about the News of the World's hacking, police involvement and any cover up and/or corruption. I'm a bit cynical about why somebody wouldn't want that to happen. It's about the press being responsible, even if they escape the force of law.