UMath1's point is simply wrong regardless of the underlying model of conductivity and even regardless of the nature of the charge carriers. The voltage is a measure of the potential energy, and it simply does NOT require any potential energy to move. His idea is wrong even in mechanics where you could easily envision large mechanical systems where potential energy does not change even as large massive objects move from place to place.
I understand the validity of your point. Perhaps you could help me understand its relevance.
When moving macroscopically large objects that are interacting with other objects, a force is required. If a potential energy function doesn't exist for that force, then the application of that force causes no change in potential energy. But of course if a potential energy function does exist for that force, there will be a change in potential energy.
In the case of moving (microscopically small) charge-carriers through a wire, a force is required because those charge-carriers are interacting with the wire. In the OP's case; as is typical of the case where the connection of batteries, bulbs, and wires are studied; that force is the conservative electrostatic force. A corresponding potential energy function does exist. So the only relevant way to move the charge-carriers is through a difference in potential energy. Or in other words, a difference in electric potential.