Futurology

Unlikely. Batteries are still incredibly expensive, also heavy and a consumable item (need to be regularly replaced). Overhead wires don't work for 1 train, but for all of them. They are also a mostly permanent installation with comparatively cheap maintenance (they are just steel+paint for the most part).

It's surely fine for a fringe route, where a train or two runs, and that would need electrification for a lot of track. So I'd assume there's a break even point somewhere.

What are you talking about?

Batteries have planety of drawbacks compared to overhead wires.

• Weight - Batteries way a LOT, meaning that locomotives need to be stronger, meaning they will be heavier, meaning that need stronger bridges and sturdier tracks.
• Lifetime - Batteries are consumed as they are used and recharged, they are also not as easy/cheap to replace as pantographs.
• Range - Batteries has limited range, normal electric trains have unlimited range.
• Charge time - Batteries need charging, normal electric trains does not.

Normal electric trains are technically the ideal transportation, you have unlimited range and don't need to carry the fuel.