Indeed there are uses of できる outside of sheer potential. Most commonly you'll find it used in the sense of completion of an action, as in your example above, where the preparations have been completed. You also see it in the sense of something that wasn't previously there coming into existence, and you often hear something like 鼻ににきびができた, or that you got a zit on your nose. You can use it generally with most instances of something that wasn't previously there coming into existence, like さっきできたパン, or 隣の家がとうとうできた. You can use it in a broad sense of abilities, too, not just to emphasize that you can do something, as in 一番できる子. There's also a phrase, できちゃった結婚{けっこん}, which means getting married while pregnant.
できる can be said, generally, to be a verb that indicates a transition of state between incomplete and complete, or a natural occurrence. In most cases you will have something at the end that you didn't have before, be it a zit, a house, or completed preparations.
If we check a J-J dictionary example, we can find over 9 uses of できる!
And as a quick ちなみに, there is another できる, spelled 出切る, means to be completely removed from somewhere/something, or to go completely out of.