I've certainly myself experienced how out-of-the-box thinking works in several ways.
The most striking is to go to bed in a totally confused state and wake up in the morning (or in the middle of the night!) with a solution that you absolutely know is a breakthrough -- and it is.
Also, when we had off-site management meetings, we always stayed over night. The next morning we usually had much more clarity.
I also got to the point of looking at an analysis and "feeling" that something was not being analyzed correctly. Intuition, to be sure, but right more often than not. When you're deeply involved for years, it becomes easy to spot what is normal, what is probably incorrect, and what might truly be a new insight. There's a wonderful book by Matthew Crawford called Shop Class As Soulcraft. Crawford distinguishes between book knowledge and tactile knowledge, which I think is what we are talking about here.
Another example that I encountered many times is to have a systems guy say "I can't figure out why this program isn't working." My answer -- tell me about it. Very often this leads to a solution on the part of the person with the problem. More often than not, I had next to nothing to add.
So I agree with you about emotional intelligence..
Here's a thought for a possible future piece -- maybe you've already done it. The question I've asked myself is whether the CFA process makes one a better analyst/portfolio manager. Suppose you absolutely mastered the material and techniques. Would that make you a superior money manager? I would argue not. I think you would be a conventional thinker, using conventional tools in a conventional manner. That would lead to a conventional result of random performance on average unable to earn back the fees and transactional costs. Sure, you might get lucky, which would assuredly convince you that you were a genius. And set you up for a fall.
You can't get extraordinary results using ordinary techniques, I would say, which goes along with your thesis about emotional intelligence. You need some special sauce, some deeper insight or intuition. The art of looking sideways.
This leads me to the curious conclusion that the CFA exams teach you what everyone else is doing. In effect, it teaches you what not to do. Now, that can be very valuable if you can anticipate how the conventional thinkers will react to a situation. But you will have at best a humdrum career, unless you can bring something else to the table:
An understanding of your client's needs and an ability to relate to them and convince them to take a path which is in their own best interest; which leads me to what I think is the most important thing a CFA can learn and internalize: A high ethical standard. I know this is the most humdrum aspect. If only others could write as interesting as Marianne Jennings about it. Even I skip the tomes of righteousness.