The article splits it, there is not a question over battery trains continuing along a branch. But article is about the bad idea of discontinuous electric on main lines and through routes.
In summary, if leave gaps, then forced to add complexity and weight to the trains for decades, so add to ongoing running costs and energy to haul the mass of extra equipment, and lose flexibility to run the pure electric trains and electric freight locos (or have to add much more powerful alternative systems to freight locos because not just moving them to depot reception off the mains).
So whilst you save in short term, having gaps on the mainline means either stuck with bimodes which as experience has shown need lots of diesel maintenance (which is so costly and time consuming the railway regularly puts trains out with dead engine) this in term loses revenue because then slow down timetables (or never speed them up) to allow the regular weaker performance. Slower timetables less attractive than trains running quickly using all their power.
Yes wires need maintenance, but costs of doing so are small compared to the costs of using diesels with their extended downtime, extra repairs and servicing and fueling, or extra energy hauling around engines and batteries which are only used part time.
He's engaging in one of the basic principles of arguing against a technology, cherry pick your examples and then assume no improvements are possible. He also conflates batteries and Bi-Modes.
If you want to create a strategy BEMU is likely the best option and it is also the option on the "right side of history". OHLE technology is unlikely to go anywhere, BEMU technology is currently at the Tesla Roadster level of implementation and is only going to get better as technology is fed through from cars.
To address a few of his augments:
Weight - Track wear is proportional to approximately the 4 power of axle weight, if we are designing a proper BEMU we are going to distribute the batteries across the carriages to equalise axle weight and thus have the lowest possible track wear. This also assumes that we are standing still with rolling stock design, if we pull technology from BEVs we are looking at having every axle powered, with a higher overall output and lower and better distributed load. We could also replace transformers with power electronics which would again remove a large point mass and distribute it around the train. Just to put this into perspective we are looking at a high performance adding about 5% to its dry weight in batteries, this is not a massive difference in track wear.
Even if we assumed a BEMU with the same weight distribution as Bi-Mode it only costs £2k more per mile in track maintenance. At German costs it would cost £1 million to electrify a plain mile of track. This would have a payback time of "infinity" once we add in maintenance of the OHLE.
Maintenance - The typical amount of maintenance done on a battery pack is zero pounds, since we are mostly talking about partial discharge cycles the battery will run for several tens of thousands of cycles, you will see its capacity gradually degrade and when this rate of degradation shows signs of increasing you schedule it's removal. It is then replaced by a much better and longer life battery. The maintenance benefit is that all the depots now don't need electrification and they also don't need refuelling facilities.
Flexibility - You can deal with failures in the OHLE or you can disable sections of it to allow maintenance while trains are still running. This is likely to be a massive improvement to maintenance cost and scheduling.
Cost - Batteries are cheap and getting cheaper, even if you double the price of a battery pack vs what you currently pay for a car pack, you assume the pack only lasts 700 journeys and then you divide it per passenger it would only add pennies to your ticket. Batteries add a small proportional cost to the rolling stock which is the cheap bit of the cost of travel. They then allow you to remove an major expense from the most expensive bit of your ticket.
Performance - You might have noticed that you can now get 1500bhp family hatchbacks due to electrification and batteries. Even though trains will have proportionally smaller batteries it is quite feasible to design a BEMU that will be able to accelerate like a tube train all the way to 150mph. Thus it doesn't matter if we lose a battery or a few motors, the BEMU will comprehensively out perform a OHLE powered train which is always limited by how much power we can put down a relatively thin wire or through substations. This plus the flexibility is why we should have BEMUs run on electrified lines and be the default for all rail vehicles.