Battery tech is there to enable this already, but scale-ability and manufacturing capacity & cost are not. That will take a while.
Power transfer will be via a 3rd / 4 rail system or via a short OLE section turned on only when activated. This type of system is now common on European tram systems. It also allows very rapid power transfers, quicker and safer than charging cables.
Some power sources will be grid fed, hence locations of OLE where that works best whilst at station stops, battery packs will slow charge & dump the power to a train when it calls.
The issue with a discontinuous electrification scheme where power is delivered at station stops is that a large amount of power needs delivering in a short space of time.
Using the figures above of 3.5kWh / carriage-mile, and assuming 10 miles between stops, and a 4 carriage train, this equates to 140kWh that needs delivering during the station stop - assuming no losses.
If we assume the train is on the juice for 60s, this means we need a power supply that is capable of delivering 8.4MW continuously for 60s at each locations. This is fairly similar to the specification for specification for a continuous OHLE systems on a high-speed line. Remember that services 12-car trains rather than four.
This poses a whole bunch of engineering problems:
* How to get a suitable power supply to each station - we're probably looking at 50kV feeder. I suspect installing these would not be substantially cheaper than installing continuous OHLE
* The load is discontinuous, single-phase. How are the phases balanced?
* Intercity trains don't stop at every station and are longer.
* The drives in all of these systems are not perfectly efficient, and neither are batteries. All non-useful energy goes as heat. Even if the battery charger is 99% efficient, that leaves 84kW of heat to get rid of
DC rails are out for this application unless you fancy a conductor rail delivering 14kA at 600V and a rectification station to supply it (hint: 3rd rail territory has similar arrangements - and a still needs a 50kV feeder network between them).
There is clearly a milage in discontinuous electrification schemes for short formation, lightweight and low-speed services with large amounts of regenerative braking, or for very short sections of discontinuous electrification on majority electrified lines. The idea as described above suffers from being both impractical, and expensive.
