Should Terror Hostages Be Given Media Coverage

Recently Paul Taggart, a professional photographer who was taken hostage in Iraq for three days back in July of 2004, wrote a story about his experience for the April 2005 edition of Maxim. It was an informative read, but I found this passage near the end of the story particularly interesting:

There were a few theories on why I ended up in safe hands rather than being executed. Most were that either a criminal gang or Shiite militants had taken me and that Sadr City militia representatives interceded on my behalf, maybe to help out in their negotiations with the Iraqi interim government and coalition forces. Another major factor may have been that my abduction was never publicized; knowing that images of me on global TV would have made me much more valuable to insurgents and in ransom schemes, the media blacked out stories about my abduction.

That’s not an angle I had ever considered before.
Right now ransoms paid by various companies and/or governments for hostages is a major source of funding for the extremists. As Mr. Taggart explained in his article, kidnapping has become something of a cottage industry in Iraq with even non-political criminal gangs getting into it for profit, which they acquire by selling their captives to the terror groups. But clearly and integral part of this process is media exposure. Media coverage of crying and suffering hostages puts pressure on governments to act. A lot of governments cave in and pay ransoms to the terrorists despite the fact that doing so only encourages more kidnappings.
So I wonder, if the media were to black out coverage of hostages taken by terrorists would this scheme be nearly as effective? Clearly the family and friends of those taken hostage should be kept informed as much as possible, but would it be so hard to limit reporting of these situations beyond that?
I’m not so sure we wouldn’t see a dramatic decline in the number of hostages taken were we to do just that.