I am on about battery and supercaps. The Chinese have a supercap train that runs with no wires or 3rd rails
As do the Japanese and British railways.
The fact that no routes have yet gone beyond engineering studies is telling.
Urban trains can start off a run on a full battery/supercap charge and get some charge while at a station. They can partially charge batteries by using mains power at stations.
The problem is the mains power circuits provided at diesel stations would simply not be up to the job of recharging the train in the 90 seconds or less it might actually stand in the station.
This becomes especially problematic on Merseyrail where a station dwell could easily be something like 30 seconds.
A 27 mile route with 15 stations gives us a stop spacing of roughly ~2.6km.
2.6km with a six car set requires something like 34kWh (2.2kWh per vehicle-km).
Recharging 34kWh in 30 seconds would require roughly 4MW of power available.
You only really have two options to deliver this power to a train (plugging is is hopelessly impractical and a cable large enough to carry that kind of power is unlikely to be easy to handle manually).
750V or 25kV.
25kV would reqiure transformers on the train and would also cause massive imbalances in the local electricity supply since it would be an intermittent load on a single phase. You would likely have to run cables the length of the line to support the system, which will cost a lot.
At 750V you would avoid the need for extra voltage kit on the train, reducing its weight, but you would need to be able to deliver a lot of amps, even if you push the standard as high it will go (since there is obviously no need to regenerate) and deliver it at 900V it will still require 4500A or something.
You would end up with 60MW of substation capacity, which would easily be sufficient to run the entire service on the line, and the only cost you would save over continuous 750V electrification would be the conductor rails. (A pair of Class 377/3s in formation have a peak power of roughly 1600kW, so you would have enough power to run 30+ six-car formations even with resistive losses).
(Plain lines don't have much signalling gear, and the kit in the stations will all have to be hardened against the currents anyway as the rail has to be used as a return conductor).
It will end up almost as expensive but without the operatinal benefits of actual electrification.
Infrastructure will only be at stations, not all along the line. The length of electrified line at stations is not a big issue, that can be calculated. That is not difficult to understand. Supercaps charge very quickly. Supercaps accept and discharge very quickly but currently do not have great energy density. Graphine supcaps do, but are not yet into commercial production, it is a case of watch this space. Batteries have high density energy storage but charge and discharge slowly. Combining the two currently can answer a lot of problems of charge and range, until commercially available graphine supercaps are available.
The limit to charging is not the limit of the rate at which you can charge the batteries, it is the limitations of the means to deliver the power to the line.
Additionally you could quite feasibly fully electrify the line with infrastructure only positioned at the stations, with the exception of the conductor rail.
Have you conveyed your negative thoughts to the Japanese and Chinese, as they have gone ahead with battery and supercap trains.
These projects are essentially pilot projects for engineering development.
As far as I know the Japanese haven't even procured additional trainsets for the existing project yet. Diesel trains still form the majority service on the route. Additionally the Japanese trains are recharged primarily while running on an adjacent electrified line.
This means they have battery capacity sufficient for running almost a full round trip, with the terminus charged used for topping up to provide operating margin.