This is terrible advice and not something I think people should be recommending to others. I love Joel's posts enough to subscribe to the rss feed (which I have never done for any site ever) but this post is something I strongly disagree with for many good reasons.
The idea he puts forth is incredibly naive and has not been taken to its natural conclusion. He talks about the negative side of keeping up with the news while ignoring the many positives.
He puts forth a simple solution to a complex problem. The solution he comes up with is naive and extreme. The problem seems to be that news being biased and overwhelmingly negative puts a damper on your mood. It can also harm productivity when becoming too engrossed in it and when the news stirs up strong emotions. His point is valid but his solution is extreme.
I think it's this kind of attitude that is making Americans stupid when it comes to civics. People in this country (the US) have no clue what's going on in the world or domestically because they either don't follow the news at all or because all they can process at any given moment is some asinine sound bite that barely comes close to touching on the substance of an issue.
Following news isn't harming anyone's mental well being. Not following the news is what causes harm. We pay a price for ignorance and the bill is about due. Following the news keeps you informed, it expands your world beyond the narrow little bubble most people live in, and it makes you an informed citizen which then gives you the tools to make smart decisions and, if you're an entrepreneur especially, gives you insight into where your next opportunity may come from.
While Joel's points about the detrimental effect the news can have and the problems with the media itself are pretty valid, tuning out is the wrong solution. The real solution is to be aware that what you see and hear is often biased. Being aware of the business side of the news will make you a better, more informed consumer of news thus making any news you consume more valuable and often actionable.
Now, if watching the news and reading mainstream news outlets creates anxiety for you then you probably have to brush up on your skills as a consumer of news. You don't need to watch 8hours of CNN or read the newspaper cover to cover to be informed. Consuming mainstream news reasonably shouldnt be detrimental in any way to you.
Furthermore, the fact that he singles out "mainstream" news makes me worry. It implies that news sources outside of the mainstream are somehow better or more true. This is not the case. Many of these news sources outside the mainstream like the brag about how they are the only ones with the balls to report the "truth". Whenever anyone appoints themselves the authority on truth it's time to be skeptical. Everyone has an agenda and while mainstream news may have some major problems with bias and conflicts of interest, it doesn't mean they are completely without any credibility news outside the mainstream can be just as bad if not worse than mainstream news. These organizations often push a very biased agenda or peddle ridiculous conspiracy theories while claiming to be sources of truth. Many times both the conspiracy theories and extreme bias go together in a news outlet beyond the mainstream in an effort to push some agenda. I used to be a believer in "truth" and conspiracy theories (often being unable to tell the difference). Now I understand that truth is not always so clear cut. There are degrees of truth.
The best thing to do is not to ignore mainstream news but embrace it. Embrace it with a healthy amount of skepticism and logic. It will expose you to new ideas and keep you up on what's going on in the world. So long as you consume it smartly you won't have a problem.
This whole post seems to be born out of a non-problem. I mean it's a problem but a problem born out of going to extremes. I happen to be keeping up with the news and in particular the US presidential election. It sometimes makes me angry but not to the point of disrupting my life in any way at all. It doesn't keep me from being productive. I listen to the radio as I drive to the train and sometimes read a paper on the train itself. Thoughts of the news don't distract me at work or socially. And when I see or hear nonsense I can tell its nonsense and go on with my day.
This post is a recipe for ignorance. If you plan to live a monastic life or a certain lifestyle that allows you to get away with being uninformed then this is good advice. But for the vast majority of us living modern lives trying to get by in this world, it's a shortcut to happiness that has a price.