Battery powered trains seem really unlikely to me. It's hard to imagine a situation where it's cheaper to do a battery powered train than a train track that supplies power (aka how most subways work).
Batteries could get a train up to cruising speed requiring a smaller train engine and less fuel.
Batteries could save on line expansion, instead of installing a 3rd rail for the whole line, they could go a 3rd rail every 50 miles for 10 miles.
I agree a 3rd rail would be cheaper in the long run. Batteries could help bridge the gap.
Some major cities in the US had overhead powered "trolleys". But, car lobbies destroyed those :(.