At the same time, a child will have no insight into the "why" behind what he/she is learning, which is natural in his/her stage of growth and development. This may explain why many so-called natural players have little idea of what they are doing during the golf swing.
Since music, or more accurately, the ability to play a musical instrument has been used as an analogy in this thread(and I agree that this is a very valid analogy), I will use it to make another point.
Music is a collection of sounds. The aspiring musician "hears" sounds in his/her head and endeavors to capture and convey them via voice or a mechanical device. While there may be the occasional savant who can do this with no training, most of us must learn both theory (the organization of sounds)/composition (the application of theory), and playing (mechanical/technical competency) to achieve the optimal results.
In other words, You need both an understanding of music theory/composition and playing skills to maximize your musical potential. A "street player" (a musician with little or no formal training) may think his/her playing is more spontaneous or inspired, but in truth, it is limited both creatively and technically. It is the trained musician (who understands music and the theory behind it, and possesses the tecnichal skills on his/her instrument(s), i.e., is not merely playing prememorized licks pulled from a limited bag of tricks) who realizes his/her potential musically because he/she does more than merely hear the sounds in his/her head, but also understands why they sound the way they do and is able to mechanically reproduce them. I guarantee you that this has a synergistic effect upon the creative process. The street player is limited in these aspects. That's why all of Chuck Berry's songs sound alike, while Mile Davis evolved musically (Miles trained at Julliard), for example.
So what's the point? Going back to the realistic potential for golfers the Hue brought up, an adult will optimize his/her results by studying theory/composition and playing as it applies to golf. Don't focus on the swing and ball striking at the expense of the other important aspects of the game. Learn course management. Really, really learn that golf is a game of targets. Understand the rules of golf and how they can help you (Tiger and the boulder at Phoenix). Learn to understand how rain, wind, the environment affect play. Learn how to play from different lies, from the rough, hardpan, wet sand, fluffy sand, etc. Learn how and when to play knockdowns, when to play chips shots forward/back in your stance. Don't be a "street player."
I have greatly improved as a ball striker via lessons and practice, but I play my best when my course management skills are "on", even if I'm striking the ball poorly.
After a year of lessons, my instructor took me to the course for a playing lesson. I played 7 holes in 90 minutes and was 2 under par (not bad for a 90's shooter!!). I was the mechanical executor of her instructions. It was her knowledge and experience and my mediocre ball striking that achieved those results.
Now, I work on my swing/ball striking, but I also study the other stuff as well. I don't worry about my "innate potential." There is more to golf than that.