There was a newspaper here in Vancouver many years ago that tried to print only "good" news. It ran out of money in it's first week.
People don't care about good news, simple as that.
On the subject of media exposing things too much, I'd say it's just as much of a "trigger" for "copycats" as anything else. Someone who's going on a rampage killing, most of the time, is not really looking to copy someone else or to make them known through copying. Someone who's going to go on a rampage is doing so regardless, they don't really need an "inspiration" for it. Censoring media to make people not go on rampages is plain stupid.
On the subject of bad news being sign of Doom, I say it's otherwise. Bad stuff making the news means people are still shocked enough by it and that they're rare enough to make the news. When we started seeing only good news, that means that the bad stuff became so commonplace that it's highly uncommon for something good to happen, thus making the news.