Generally, I agree with this, but I don’t think it’s nearly as simple as you write it out to be. For example, thinking about how you can solve a problem can often spread itself out through a huge range of other thoughts, some of which you may not even recognize are directly connected to trying to solve the problem, but do end up being an important part of your solution down the road.
Let’s just examine some of the ones you drew out in your header: “I suck”, “what if I fail”, “my life is over”, and “does he love me?”. You could say that these thoughts are not directly aiming at a problem, however any one of them could be the start of a thread of thought that does, and cutting that thread short is dangerous and counter-productive.
Perhaps you failed at something recently. Often times, the first thought that goes through my mind is, “Shit, I blew it.” However, that naturally transitions into “Ok, how can I avoid blowing it in the future” by the time my train of thought has ended.
I think that the sentiment you are getting after with this piece is good, but the actual advice given is just a little bit off. Your goal is to move people towards practical action and solutions to issues, and this is excellent. As a solution, you propose filtering your thoughts to cut off anything that isn’t dry logic, but this can be harmful. People need to feel emotion, need to evaluate themselves and their lives, and get a feeling for how things are going. However, you could help to push readers towards the same goal by modifying your implementation advice just a little bit. Instead of advising readers to cut off any unproductive thoughts, advise them to set explicit goals for the end of each train of thought as it arises, and make those goals be “concrete solutions and progress for the future”, for the most part.
For example, someone may start feeling badly about themselves because they were in an awkward social situation. Cutting that thought because it isn’t productive is unhealthy and prevents potential future improvement. However, recognizing that your goal is to avoid awkward social situations in the future and letting the feelings and thoughts ride out their course is perfectly fine, so long as the conclusion to the train of thought is an overview of how things could go better in similar future situations.