I agree that folding karambits are significantly less versatile as martial tools than fixed blades. Here's why:
If you look at a well-designed fixed-blade karambit, you'll find that it is typically double edged and/or has a series of teeth on the convex edge. In many cases, the blades have a more gentle curve--alomost a banana shape. On the back of the handle--adjacent to the ring--there is often a slight concave section, sometimes called a "brake." If all these features are present, the concept is that the "spinning" action of swinging the blade out to extension on the index finger and then back to a reverse grip offers the potential of multiple cuts.
To understand this, imagine starting with the knife in reverse grip at a distance from your adversary. He thinks you're out of range, but by snapping your arm forward and spinning the karambit out, you strike with the sharpened or toothed back of the blade with an unexpected extended reach. This tactic is also one reason that the blade cannot be too radically curved. If its curve is too tight, the outside radius of the cutting edge defines a near-perfect circle when spun, creating a shallow, ineffective cut. If the blade is straighter, it cuts deeper.
In the extended position, the next potential cut is to use the convex cutting edge. To do this, the index finger maintains control of the knife and the back of the handle is braced against the front of the knuckles. This is where the "brake" comes in. If there is no relief cut for the middle finger, it becomes a fulcrum and hard cutting pressure will break the finger. In all fairness, I have seen some karambit styles and martial arts systems that use karambits without "brakes." They do cut with the convex edge with the blade extended, but focus primarily on linear pulling cuts rather than arced cuts, minimizing the pressure on the middle finger. Still, having actually done cutting tests with a variety of karambit designs, my middle finger and I very much prefer karambits with brakes.
The final type of cut is the most basic and powerful. Swing the knife back into a solid reverse grip and cut with the concave edge. If you look at many systems of silat, you'll see unusual punches that hit from angles or "wedge" the opponent's arms out of the way. In many cases, these movements represent the use of the karambit in this solid grip. No spinning, no fancy stuff--just punching or wedging "past" a target with the fist while plowing through with the blade.
With all this said, the shortcomings of a folding karambit should be clear. Smacking an armed attacker with the unsharpened back of a blade and, in the process, tempting the blade to close is just not a practical tactic. If the handle design isn't comfortable for pull cuts, you will injure your hand if you try to do them with power. Your most effective cuts will be the ones you can deliver with enough power to cause debilitating damage to your attacker--probably the ones delivered with a full reverse grip. That's why, as Bladekeeper rightly pointed out, many traditional karambits did not have rings. Others had rings with extended tabs or spikes for striking that made spinning them impossible.
I hope this helps. Karambits can be great fun. Like balisongs, they are yo-yos for knife guys (and gals). And, like balisongs, you shouldn't confuse dexterity and physical manipulation with combative function. Sometimes they are the same--sometimes not.
Spyderco Special Projects Coordinator
Founder and Lead Instructor, Martial Blade Concepts