Nobody's stupid enough to do that except the Bush administration, and a press badge doesn't grant you access to black sites. If anything, the Iraq War was a perfect example of how well the American military can keep a secret when they need to, when it was only online document leaks that confirmed the existence of groups like Task Force 373. There were some small leaks by the press, like the stuff on Guantanamo Bay prisoners and Abu Graihb, but in the overall scheme of things they were largely too small to have a significant effect on the public consciousness, and they took too long to mature.
As for whether free press should be suspended, I think moderation should probably be used. A lot of the people who took photos in Vietnam of supposed brutality of American soldiers or allies, like the guy who took the Nguyễn Ngọc Loan execution photo and Jane Fonda after the Hanoi Jane incident frequently came out and said they wished that they never took the photos or had them published. Ironically in most cases it wasn't some morality which guided journalism in Vietnam but rather capitalism itself, since such pictures sold millions of copies of papers and magazines. At any rate, I think the mistakes from Vietnam have been learned, both by the government and by media corporations.
It's not conventional journalism that policymakers need to concern themselves with anymore anyways, since Twitter and Reddit have given birth to an entirely new form of journalism that can be anonymous and instantaneous. If anything, the saturation and ability for online sources to give such wide ranges of information and opinion would dilute the effect on the public consciousness as a whole in wartime so much so that an oversaturation of a particular opinion in a muddy case, like in the Vietnam War, would be exponentially harder to attain.