It's like music, some intuitive ones are great and creative, while some who understand music theory and can read music have no innate talent. The words come naturally for some, while others construct a sentence and look at it like a mathematical formula. If it doesn't read right, it isn't written right is the intuitive way and that is grammar.
Then there are those who bring both to the table: impeccable mastery of theory and an amazing inner voice. Those are usually the pinnacle of the art: Mozart, Ravel, Stravinsky. Sinatra.
I fundamentally disagree with your last sentence. Untrained intuition is somewhere between erroneous and dangerous, and it is always self-indulgent. Grammatical (stylistic, syntactic, even orthographic) intuition, if it is to be of benefit, is built on a solid base of knowing the rules and the various irregularities. For it to sound right, it generally has to
be right.
Some great poets deliberately say it wrong in order to evoke something not easily or concisely done otherwise. However the poet was fully literate, as is his intended audience.
Many people think that poetic license extends to less rigorous forms. (Numerous examples are known to most of us here as awful rock lyrics.) However, the result is usually not as evocative as the author would like, but simply disjoint.
Intuition without the full surrounding embrace of discipline is a prescription for dissonant error, and the results are quite often unattractive. They are always an offense to the simple virtue of literacy.
