how would you go about proving (or disproving) that electric companies and the like are (or are not) natural monopolies
One of the ways that I would suggest that power companies are not monopolies is simply the fact that in some markets, particularly major cities on the East Coast, a consumer can choose their power supplier from among a host of different companies. These are all dependent on the utility in order to deliver the power but they contract with various power production entities in order to "purchase" electricity and then sell it at different rates to consumers depending on what they need.
On the other hand, all of them are dependent on the utility, often state supported, to actually get the power from the generating entity to the customer and so the utility has a massive amount of control over the situation. Without the infrastructure of the utility, which of course they own and control and repair in the event of damage, etc., it matters very little who is buying or generating or selling the power, the utility controls the delivery vehicle and in turn the good being delivered, in this case power.