I think that the opinions on opportunities for charging batteries on an operational electrified main line are in general unduly pessimistic here. Clearly the issue doesn't really exist on an OoLE equipped mainline. On a 3rd rail line, there can be issues if charging is simply allowed on demand as even on a 10,000A line supply, the current could get near to the limit with more than 2 trains in the section, - but only when they are using maximum power, i.e. during acceleration or climbing long gradients. The rest of the time, trains like Electrostars moderate their power to maintaining a set speed (moderate demand), coasting (very low demand), or braking (returning power to the 3rd rail). Now if the battery trains had charging managed according to local conditions in terms of availability i.e., the number of trains on the section, (probably reflected in the line voltage), the topography of the route, (gradients, acceleration zones from stations and junctions/PSRs) and any other relevant local features, the charging cycle could be accommodated within reasonable limits. Local charging authorisation could be enabled by track balises that wewre read when the battery train was in a 'managed' mode. When 'on demand' charging was permitted, an end of zone balise could authorise the train to do so.
Managed charging of batterieswill be a big thing where legacy networks and supplies are taking on large uncontrolled loads, e.g. home charging of EVs, so the technology will be available and mature.