Sorry but this is extremely misguided. You are making assumptions that make you look like you haven't talked to a mathematician as if they were a person, but a

Sorry but this is extremely misguided. You are making assumptions that make you look like you haven't talked to a mathematician as if they were a person, but a machine or a misterious magician. Mathematicians do not find difficult to verbalize motivation and intuition because they (we) are autists. We struggle to do it because it is really difficult sometimes. You can find that you have an intuition that you cannot put into useful words (sometimes the intuition is "it should be like this"), or that it relies on more advanced concepts (something that clicks only when you get to know concepts that rely on it), or that you know that the idea in your head is not useful to others and putting that down in a book would make things worse. I have not written any book, only some notes for other students, and with that I already know it is difficult to write a good motivation and intuition to abstract concepts even when you completely dominate them. Moreover, most of the mathematicians learn to develop their own intuition and motivations and it is not as important to write yours (which are subjective most of the time) down.