What’s the proposition to “electrify” trains? Batteries or a live wire everywhere there’s train tracks?

Both seem really inefficient to me with our current technology.

Yes, around the world electric freight locomotives are powered by overhead lines, and more occasionally by a third rail. It is a mature technology and the US is an exception among industrialized countries (China, all of Europe, Russia, Australia, Japan, etc) in that they use only diesel for freight.