Oh yes, Northern commuters should definitely stop moaning that commuters are shoved into two-car rolling stock that even the Islamic Republic of Iran didn't want to subject onto their own citizens.
Even when adjusting for all other factors, London and the South East has an absolutely ridiculous advantage in per-capita transport spending. Even by their best estimates, Barking Riverside will only benefit 25,000 people. Transpennine electrification, at twice the cost at most, will benefit a hundred times as many people.
I never said that Northern shouldn't have been given more investment, in fact I agree that the Pacers should have been replaced a long time ago.
With regards to numbers of people that will benefit there is a difference between the number of people who live in an area and the number of people who will benefit for a station/service by using it. If there a new service between a fairly major city and a small, mostly residential, town although the service would have a catchment of say 500,000 people it would only really benefit the 6,000 people in the small town.
Now depending on the time taken to dive into the city it could be that the train isn't very competitive, add in fairly easy parking and the service is likely to be poorly used. Based on your argument that service should be funded over a service linking two much smaller places which has a busy rail service already because it doesn't "benefit as many people".
As I have said I don't think that some people understand just how many rail passengers there are in the South East. You talk of people being rammed into Pacers, which if they were extended to 4 coaches would probably have lots of space. Yet there are trains heading away from London in the morning peak which between Woking and Guildford (the last stop for half the services) are full even though there's 4 trains an hour all of which are between 8 and 12 coaches long. Even trains that arrive to Guildford before 8am have few spare seats. Yet Guildford has a population of less than 100,000 and so by your definition shouldn't see improvements.
Yet in the evening peak there are trains which are 5 coaches long which are often full and standing from Guildford to Woking. The train is so busy that it often runs late because of the number of people getting on and off at both Guildford and Woking. Yet even with 4 tph and most trains are 10 or 12 coachs there's still need for more coaches. However, even off peak there are lots of 4 coach trains (again on 4tph) which have people standing.
The reason for it, is that although Guildford has a similar number of passengers as Newcastle it has 1/3 the population. As such any improvements for Guildford would benefit the times as many passengers as Newcastle. Within London the ratio would be much higher.
As such sine like Barking Riverside although may only have a population of circa 25,000 it could benefit as many passengers as somewhere with at least 3 times the population in terms of passengers who benefit. In fact TPE electrification is likely to only benefit something like 100th the number of passengers that Barking Riverside would add only a tiny fraction of some of the large places it serves will use those services. Whilst a massive number of the small number of people at Barking Riverside would the service.