*BBC (UK taxpayer) and Economist (subscription) are among the exceptions.
Here's a 2008 article pointing out that news' focus on the moment is also a significant failing: http://www.overcomingbias.com/2008/03/against-news.html
This 2008 article also points out the social function of news: as a common topic for discussion, particularly for determining compatibility with others (whether of belief, intellectual interest, etc)
The HN article makes a great point about how much this info effects you. If news media let their audience know that nothing happening right now was likely to effect their lives in any way for at least a week (at best, more likely never), then audience would only tune in once a week, which drops viewing figures by 86%. Also, only checking news once a week lets the information settle, and often key details emerge which negate previous reports.
Another useful trick, if cold turkey is too much, is to put a one-day or one-week delay on all incoming news (ie waiting a week to read newspapers). If nothing much is lost by a weeks delay, then its easier to go cold turkey.