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This is true.
One of the remits of the Docklands Light Railway was to extend to those 'forgotten' areas in order to promote their regeneration.That could work elsewhere in the UK, but one of the reasons it worked for the DLR is that the people who lived there (or might be persuaded to) still wanted to get to other DLR stations on a regular basis (e.g. Bank, Canary Wharf). I'm not sure what you do when not enough people want to go to anywhere on the line.
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True. You end up with a chicken and egg situation though in that these places have low populations, in part, because they have such poor public transport.
From a pub/armchair perspective with zero knowledge on the topic... this is why investment in Internet connectivity and renewable energy unreliant on traditional infrastructure is so important.
My hunch is that the cost of better Internet would be lower and deliver a greater ROI than better public transport.
Isn't this why Frome is the new Shorditch?
Investment in PT is driven by utilisation which in turn is a function of population density.