Electrons do move through the wire. They travel on average much slower than the actual energy does, but they do move.

You might be thinking about how the energy isn’t carried by the electrons. The electrons move, which create a field on the outside of the wire, and the field carries the energy.

This is why, for example, when the power plant shoves some electrons through a wire, you don’t have to wait for the electrons to travel all the way through the wire and into your house.

The electrons get pushed into the wire, which pushes on the next electron over, which pushes on the next one, again and again, until finally an electron in your home device starts to move. Generating a field which your device uses. Even though the original electron that the power plant pushed into the wire is still probably inside the power plant.

It is a bit more complicated than that in reality, it’s not just one electron pushing into the next one, it’s an overall movement of charge that on average moves through the wire.

But the electrons do move through the wire, but each electron doesn’t carry any energy, it’s the physical movement of the electrons which generate a field which carries the energy.