This sounds like an explanation for the old adage: "Go with your gut". If your brain is a lot better at recognizing patterns than it is at drawing conclusions through a chain of reasoning, it seems advisable to trust that which your brain excels at. Something similar is brought up in The Gift of Fear, where the author cites examples where the pattern-recognition signaled danger, but people ignored them because they could not come up with a chain of reasoning to support that conclusion.

Sufficiently high quality mathematicians don't make their discoveries through reasoning. The mathematical proof is the very last step: you do it to check that your eyes weren't deceiving you, but you know ahead of time that it's your eyes probably weren't deceiving you. Given that this is true even in math, which is thought of as the most logically rigorous subject, it shouldn't be surprising that the same is true of epistemic rationality across the board.

Interesting that you bring up this and Poincare's experience. Jacques Hadamard wrote a book examining this phenomenon based on information he gathered from other mathematicians as well as his (layman's) knowledge of the psychology of the day. His conclusions bore several similarities to what you're trying to explain in this post. He did, however, note that experiences like Poincare's generally only took place if the researcher in question spent a lot of time working on the problem in the old "chain of reasoning" way, with the pattern often becoming clear some weeks or months later, after the researcher had moved on to a different problem. Perhaps this is what constitutes training one's brain to see patterns.