I agree that the press should be regulated by the state, because in general, or at least examples that I've seen when reading the news reports in England, the press are ruthless in their pursuit of a story, often at the expense of innocent people. If the press is regulated, it will avoid people being hurt and exploited just for something to make a good front cover story.
What this question comes down to is censorship. Our constitution was written to defend against this. A free press is the cornerstone of a free people. When ideas are controlled, so are people. The State operates under a cloak of secrecy that is rarely pierced by a heavily redacted FOIA release. If the State controlled the press, these rare glimpses would be gone, as would any meaningful discussion of anything.
The press should always be free from the state. The free press, or the fourth estate, is intended in a democracy to provide a means of outside criticism and reporting, most importantly in this discussion, of the state. It is vitally important that the state is not allowed to operate without outside overview; this provides a means in which accountability of politicians is maintained, and in which corruption can be ousted. Regulation of the press subverts this important part of the political ecosystem, and in extreme cases can lead to a loss of open democracy.
No, the state should not regulate the press. Freedom of the press and freedom of speech are part of the foundation the United States was built on. State regulation of the press would cause a myriad of problems. If different states applied different regulations to the press it would cause mass confusion and outrage. Regulation of the press by the state is not in the best interests of the United States.