No one is going to hire a golf course designer without a track record - and the only way to get a track record is to work for another designer. (unless as others say you are putting up the development $$ yourself or have a mad rich uncle bankrolling you)
As far as education go, you can lambast the landscape architecture profession all you like, but it does give one an appreciation and understanding of design and the design process (if nothing else!). Civil engineering also would be good for teaching you about earthworks, drainage and a methodical way of thinking. Neither degree gives you all the skills required but they (coupled with an interest in golf, golf design and some personal fortitude) can get you into the position of an apprentice with a golf course architect.
The trent jones approach (and I think Doak also) of selecting courses from one or another of those schools is probably the best and most rounded approach but is only for the "preordained" golf course architects amongst us. At least finishing a degree gives one something to fall back on should plans go awry. (anyway, once you have been designing golf course for a few years you are pretty much shot for any other sort of design). The same goes for the shaping approach, at least you are in the feild, learning skills and meeting the right people - should the moons be in alignment and everything fall into place you might just find yourself helping design a golf course....more chance there than if you are outside looking in.
After the education process(LA., CE or School of Dirt), you need to work for a designer to round out your education, learn the process of golf course design...as well as the politics of it all. Despite the success of Dye, Tom Doak and Crenshaw & Coore, the ability to grade (on paper) a golf course to your vision is a skill that is required of most golf course architects. Sure, you may be able to get around this skill with the right projects and clients, but don't hold your breath.