Conducting in particular is essentially based on this. Lots of people are trained to analyze the forms and harmonies of scores and read the whole page at once, but the conductors job is to understand what the purpose is of every note in the score. The conductor needs to find out what emotions the composer is evoking, and how to portray those emotions and simultaneously take the music the directions it needs to go. Complete humility is required to think this hard.
When I perform or write my own music, I keep this in mind as well. The hardest thing as a jazz drummer is to not be even the slightest bit self-indulgent. Every member of the jazz combo has to find the point right in between being trying to direct the music by being overly showy and letting the rest of the ensemble carry you somewhere. This requires a constant and neutral focus on the development of emotions and sounds that are created by the group.
Critical thinking is one of the core values of musicianship. Open mindedness about musical ideas must always transcend one's ability to perform the notes on the piece of paper.