Edit TINYURL destination on free account [closed]

On the free tinyURL account, a link which you created cannot have its destination be edited. If you try to delete it, it tells you that it will be hidden from your view, but it still exists.

However, the alias CAN be renamed. I was hoping that by renaming it, the original alias then becomes available to reuse in a new link.

Was I wrong to assume this? Or does it take a while for that alias to become available again? Or is there another solution?