Because that's when legumes are considered ripe - when they are dry.
If you have ever grown and picked your own legumes, you'll know that they are left on the plant until fully ripened. At that point, the pod is dry like straw, and the seeds inside are hard. They are then harvested and stored as a convenient shelf-stable crop. These are the "dried" chickpeas you refer to.
There are a few legumes which are bred for producing a fleshy pod, and they are eaten at a different point in development. A typical example is the green bean. There, you pick the pod when it's at a already-thick-but-not-dried stage, and cook the pod, along with the rudimentary seeds inside. I'm not aware of any such cultivar having been bred for chickpeas.
The first kind of legume can in principle be picked and eaten while still unripe, but that makes little sense. The grower would be sacrificing both caloric potential and shelf life, two factors which were quite important among subsistence farmers.
Two exceptions (that I know of) have happened to establish themselves - peas and edamame, and I think both of them were quite local before globalization. In both cases, the seeds are eaten at a "fresh" stage in addition to being left to ripen into dry peas and soy, respectively. A credible explanation of why exactly these two happened to have this rare fate, while others didn't, would require a large research project for a historian, and is thus out of our scope. But to sum up, there is no good reason to expect a random legume to be cooked in an unripe state.