Hi mumof2balham, thanks for reading my analysis. I certainly don't envy a commute from Clapham South on the Northern Line - my time on the Northern was from a station a lot further south.
"why would someone bother going via Angel to go to Bank?! Taking C2 to Tottenham CR and change for the Central Line to Bank would be much quicker (in addition to be a nicer journey)."
The analysis I've performed is a deliberately simple approach, that tries to find the shortest routes between two places with CR2 open. Since Balham to Bank via Angel is possible, the computer program calculated a result. Would anyone use that route, probably not, but the program was providing options, not making decisions. I'd also note that the quote above assumes that the Central Line has lots of available space in rush hour.
For the record, it is my opinion that TfL should be providing this data to the public, not me. (They have far more sophisticated tools available than I do.)
Of the two conclusions, the first is self-evident really. "No one already on a Northern Line train approaching Balham and heading to London Bridge, the City or Canary Wharf will change onto Crossrail 2. " All this says is that for anyone going to London Bridge or Bank that boarded the Northern Line at Morden, South Wimbledon, Colliers Wood or Tooting, they are already on a train going exactly where they need to go. Changing onto CR2 and then changing again seems highly unlikely (some of those people will even have seats!).
The second conclusion is more contentious. "Anyone on a Crossrail 2 train from Wimbledon and heading to London Bridge, or the south part of the City will change onto the Northern Line." As you say, whether this is true or not depends on whether people getting off CR2 can actually get on a Northern Line train.
The key point here is that my analysis is attempting to challenge a claim made by TfL. They claim that CR2 at Balham will reduce crowding levels on the Northern Line by 1.2 people per square metre (crush crowding is around 4-5 people per square metre, so thats about 25% less standing commuters per train). Logically, if TfL are right, then there will be space for people to transfer off CR2 and onto the first train on the Northern Line at Balham. And for London Bridge, the Northern is definitely the best option. For Bank, there will be a choice of changing to the Central Line, but is that better? The numbers say that Wimbledon to Bank is 25-27mins changing to the Northern or 28-30mins changing to the Central Line. Will people trade 3mins to avoid the Northern? Will the Central Line have any more space available than the Northern? These are the really tough questions.
What concerns me most is that journeys that CR2 should relieve, such as Morden to Victoria or Euston, get very little journey time savings (eg 2-3 mins). This raises the possibility that those journeys may continue to clog up the Northern Line. As you say, some people will decide to change to CR2 because it will have more space, and trade a few minutes for more space. But how many?
The Northern Line desperately needs relief. But I hope I've also explained how even with TfL's claimed 1.2 people per square metre relief, it is not exactly going to make the Northern Line pleasant. Ultimately, it is up to TfL to justify their claimed relief, not me.