But Twitter doesn't do good news either. I know that because I always turn to the news section, and there's a story that a day or two old. It's already been published in the newspapers.
Also, I happen to have a subscription to the Washington Post, and so I can click on its links in Twitter. But if I didn't have a subscription, I wouldn't be able to read the news. New York Times is the same.
It's better to just go straight to the news sites.
Often, when I'm looking for something that I know is breaking somewhere, I look at Twitter. It's impossible to find. I'll find some on youtube and some on Google News and some in various newswires like Reuters or Associated Press.