In truth, most gca's do not have great handicaps. I know, as I ran the ASGCA golf tourney for a few years. Some are quite good, and others are really terrible. Most are typical mid handicappers.
Design is really a separate skill set from playing, so there is IMHO, no real connection. Obviously, the architect must understand the game, which doesn't necessarily require the ability to " execute the theory." There have been a lot of really bad courses by those who got in it from a land planning perspective, or engineering perspective, etc. On the other hand, there have been some great courses by hacks. So, it runs the gamut, much as golfers run the gamut from serious as Hogan to funny as Zoeller.
As recently discussed, Tour Pros have no clue (in general) and are usually at best, editors to the design. Even a trained gca who is a good golfer presents some problems - the good players almost inevitably tend to design the harder courses. While we still need a few of those, sometimes we get them when and where we don't really need them.
In the end, its probably a good thing that the handicaps in the gca ranks tend to reflect the handicaps of the golfing public in general. Then, its just a matter of picking the right gca for the job at hand.