What Erika posted is spot on. I'll just add that 1- and 2-bone IK constraints are deterministic: there is only one solution. When there are more than 2 bones, there are many solutions, meaning there are many bone rotations that result in the tip of the last bone being at the IK target. That means the pose resulting for more than 2 bones is dependent upon the pose in the previous frames.
That creates a number of problems. For example, if we want to pose a skeleton in the middle of an animation, there is no previous pose. We could do something like start from the setup pose, but the result is unlikely to be the same as if we had played the animation from the beginning. Playing it from the beginning and posing it on multiple frames so we have the right pose in the middle of the animation would be a lot of computations.
Lastly, as Erika mentioned, getting exactly the behavior you want from IK with more than 2 bones is difficult and you are usually better off animating it in other ways.
