So I am a big fun of randomness. I believe it helps much. Especially obvious is its help in creation of art and music. I combine randomness with optimization. My method is very empirical. Start anywhere at random, optimize the process by changing parameters, if nothing works, start at random, but far from the location of start. Repeat optimization. Keep testing random locations. Repeat the process several times and see what happens. You may notice a pattern in response of the results to almost random input. As you see the pattern, optimize and test it, see what comes out. This approach works great if there are too many unknowns to account for and if you are capable to see patterns. With my intuitive mind I see patterns pretty well. So the method works pretty well for me. I don't think people with logical mind use it a lot. I optimized this empirical approach in my experimental science work, where I have a structured and documented the process of discovery, but also in other parts of life. I would think that many people have a similar approach, females slightly more than males, engineers and experimental scientists use a lot of empirical approach. I see the traces of use of randomness generators in many works of visual art and in poetry, so this approach is somewhat spread in humans, it seems to be a general theme especially among creative people and experimental scientists.
I would think that you know much more about the mechanics of thinking and about what happens in our intuitive thinking than we do, so you may appreciate specifics of human intuitive mind and draw conclusions from it.
Interestingly, in Nazi Germany, people with fussy thinking were diagnosed with a diagnosis of "feeblemindedness" and were sterilized and prosecuted in large numbers. Also Interesting is that "feeblemindedness" was associated with dissidence. Besides, Nazi Germans were prosecuting Jews for similar traits - dissidence and alternative thinking. I wonder maybe Nazi Germans were prosecuting "feebleminded" because the intuitive, diffuse, fussy, uncertain way of thinking naturally resists brainwashing by mainstream propaganda and gives rise to dissidence and alternative way of thinking. This idea is consistent with the observation that Einstein was also a daydreamer and his thinking seems to have been very much intuitive and exhibiting feebleminded qualities.
I hope that you will find our intuitive thinking interesting and that you may find similarities between our intuition and your thinking practices.