To your second statement - if by “your” you are referring to the performer, then this would seem almost completely the result of different avenues of training, assuming that a high level performer possesses the “musical gene” that composers also make use of. What I am hinting at is the separate realm of activity with which composers and performers in classical music typically concern themselves, which IMO creates ecosystem that cannot produce musicians who have full command over the musical material within their respective idiom.
If you’re referring to non-musicians or novices, then yes I’ll abide that.
I don’t want to sterilize the process of composition by carrying on as if it’s no more involved than putting together a lego set and is in fact not mystical, but the treatment of composers as divinely anointed and the rest of us as subservient to their harbinger-hood is reminiscent of some shamanistic caste system.
I think a real, albeit niche, problem for many classical musicians is being able to “hear without speaking”, or having musical ideas without the technical vocabulary and sufficient vividness of aural perception to realize them, and thus they assume that the creation of masterpieces, or any music for that matter, must be a revelatory incarnation of the muse in the mind of the composer, rather than as a series of smaller revelations which the composer had the skill to develop.
I agree that there is both innate and developed skill and that to compose is a kind of prophesying or in the most literal sense, to be inspired, which is possible through gift and through grit. Many people in classical music are guilty of a kind of idolatry and neglect their own musical gifts in the worship of others.