Once you realize that idle brain time is when actual creative problem solving occurs without you conscious of it then its easier to let go. I definitely feel fine just staring out of a train window rather than my phone knowing this.
The way I view this is that there's no such thing as idle brain time. When you take away focused conscious thinking, the brain is built to do background problem-solving on its own. (This also makes sense if the purpose of dreaming while asleep is garbage-collection of unresolved thoughts and anxieties.)
