I can think of a few usages for it.

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.

The rest of the world doesn't live in high density built up areas. Many small crops farming trains in rural areas can not and will not be allowed to run power through the tracks in above ground situations.

The rest of the world uses overhead lines for powering trains (I'm a bit shocked to learn that this is not the norm in the US, actually)

At least in the UK, a 3rd rail was common. IDK about the rest of the world but wouldn't surprise me.

Some major cities in the US had overhead powered "trolleys". But, car lobbies destroyed those :(.