That's a direct grab from Excel rather than a presentation slide. The analysis has a charge curve included in it so you can see that it charges faster when the battery is depleted and very slowly between 90-100%.
If the number in the "dwell time" column is greater than zero then the train took a charge in that station, I can manipulate the analysis by manually putting a zero in that column if I don't want it to charge at that station. You can work out how much goes in at a given station by looking at the SOC on entry and exit.
Some of the station stops with a 0 dwell time are passing stations which are used to count when 25kv sections end and begin.
Most of the stops on this line don't make too much difference, I've done a simulation where the train doesn't charge at stations without 25KV already in them except for the terminal station in Cleethorpes. I've also made this an equilibrium cycle for the battery in that it starts and ends on 90% in Liverpool.
The cycle is pushing it a little as it is coming into Cleethorpes on 10% charge, these are end of life batteries so I have accounted for degradation, but that's still probably too little margin. You would want either some more electrified sections, a more efficient train, a bigger battery or some more charging stops.
The key point is that there is a lot of optionality and my money is on battery trains happening quicker due to replacements and conversions than full electrification. Also for short dwell times I expect that rather than an island piece of OHL with a substation we'll probably see a battery at the station charged by an existing grid connection rapidly discharging into a train over 1-2 minutes then slow charging back up for 10 minutes before the next train comes.
I'd argue that it's no more necessary than a range extender on a Tesla.
Some things to consider, that BEMU I describe has a 2175 KWh battery (It could be much bigger but I'm being pessimistic rather than imagining what a purpose build BEMU would be like), it has an operating range of 126 miles on ECML average consumption.
In general we don't want to routinely discharge its batteries below 10% which means that we have a 12.6 mile range buffer at all times. However that figure is at express passenger line speeds, if we want to trundle along at 50mph then the range is much longer given that energy usage goes with square of speed then we are looking at more like 75 miles in contingencies. That should be plenty enough to get the train back to a wire or a charger.
Given the rate of charge speeds its also likely that just adding a few more minutes of charging at a platform and/or running a little slower would give the train enough range to leapfrog a section of electrified track which is faulted or a station with a broken charger.