Your reading says that these vessels were not used as batteries in ancient times. But the arguments used in the reading are not convincing. The battery explanation could very well be correct.

First, about the absence of wires or other conductors. Remember: the vessels were discovered by local people, not archaeologists. These people might have found other material located near the jars, but since they were not trained archaeologists, they may not have recognized the importance of that material. So material serving as wires or conductors might have been overlooked as uninteresting or even thrown away—we will never know.

Second, it's true that the copper cylinders in the vessels are similar to the cylinders used to hold scrolls. But that does not really prove anything. It's possible that the copper cylinders were originally designed to preserve scrolls, and that some ancient inventor later discovered that if you use them together with iron rods and some liquid in a clay vessel, they will produce electricity. That's how the first ancient battery could have been born. In other words, the copper cylinders could have been originally used for one purpose but then adapted for another purpose.

Finally, there's the question of the possible uses of the battery in the ancient world. Well, the battery could produce a mild shock or tingling sensation when someone touched it. This could very well have been interpreted as evidence of some invisible power. You can easily see how people could convince others that they had magical powers through the use of the battery. Also the battery could have been used for healing. Modern medicine uses mild electric current to stimulate muscles and relieve aches and pains. Ancient doctors may have used the batteries for the same purpose.