I've wondered if battery electric multiple unit trains will/would make electrification cheaper since you then don't have to electrify the whole line. You can avoid having to put overhead lines where inconvenient, expensive, or potentially dangerous as well. Like tunnels and stations.
I love this idea, are you thinking a hybrid model? i.e. Overheads where possible, battery to bridge the gaps? that way in some places the trains could charge en-route.
That's exactly what I think is interesting. It's actually an old idea. I think with modern batters the design becomes a lot more viable. There are already some of these in service and more on order.