Jim,
I said somewhere here that the first qualification to be a gca is whether or not you let someone talk you out of being a gca. The second is being optimistic enough to believe you can do it, and naive enough to believe you can't fail.
Ask most of us, and we will say what Tom did - you have to really love golf. Although, I will say someone surprised me once by asking IF I had to choose, would I prefer to play golf or design golf courses, and it was actually a pretty easy answer for me - I would design golf courses.
In addition, I think the one thing no one has really mentioned here is that you really need to have some natural ability to design things. Designers just think a certain way. There is such a thing as a design personality. For instance, I told all my employees I would know in six months if they had what it took to work for me. In truth, I only looked at ones with a great college portfolio, and even then, it took about six days most times to form an opinion.
Just as playing golf at a PGA Tour level really doesn't make you a designer, neither does being able to grow grass, do engineering, or for that matter, be a landscape architect, although the latter has the closest curriculum you can find. And, more importantly, could teach you whether you seem to have any design ability. In taking with other LA grads, over many classes and many universities, most say that the cream of the crop rises, and that you could tell which of the students was going to be a designer some day. In my class, 8 of 11 who started in LA as freshmen (about 45 in all) and got a degree went on to own their own firms, 2 became park directors of some kind, and one was a campus planner. I imagine the same weeding out process happened in the Dye organization - and nearly all others.
Even an LA degree doesn't teach you to be a gca, even though it imparts some basic skills in grading, drainage, turf and soils, surveying and aerial photos, etc. if you tailor your degree. That said, I recall that an intelligent person with an interest in the field can learn. There is plenty of evidence that Jack Nicklaus, for one, picked up all the technical details, even if he spent little time drafting. In the end, I doubt anyone learns to be a gca other than the process you, Tom Doak, myself and most others go through of being an apprentice to someone who knows the craft and who really teaches you how to build a golf course. And, even learning the design principles of balance and composition can be inherently known by a design personality, regardless of degree.