[TekMol]

But you do lose energy as current flows.

When you start with 10 elecrons on the left of the wire and none on the right and end up with 5 on both sides, you lost all energy that was stored in the system.

[desmond1303]

The mind-blowing thing is that electrons, as far as I understand it, don't actually flow through wires at all. If they did AC power would be pointless

[actionfromafar]

Well they do but very slowly. With AC they just wiggle left and right.

[htfu]

This is some kind of a simplified view of how a battery works. It is not how an electric field functions.