If you truly believe this, then you are seriously misguided.
A clear illustration of how wrong you are lies in the historical account of Wolfgang Amadeus Mozart. Nobody trained him, taught him or molded him. He simply began listening to other musicians play and he learned it on his own amazing account.
He could write entire symphonies out of thin air, without outer influence and he only wrote them once, without the required proofreading or editing. He could also hear an entire musical piece only once, and then duplicate it perfectly and in it's entirety, find flaws in it and correct it while he was playing it.
His genius was entirely spontaneous as was Einstein.
You gloss over the fact that Mozart listened to music before he played or wrote it. He knew what music was. I do not intend to get into a nature/nurture discussion here. There is no question but that he was a musical genius. His ability to write music on a sheet of paper was learned. His knowledge of the mechanics of music was learned.
I am not talking about developing mechanical skills. I am talking about the development of critical thinking, so called intellectual activity. There is no particular reason to call Mozart an intellectual genius though he may have been. Mozart’s musical genius is not a function of intellect, at least not in the sense I am using the concept. Your argument unnecessarily muddies the water.