I completely agree that Stocksbridge to Chesterfield should be heavy rail and extended through to Nottingham allowing the current Sheffield to Nottingham service to drop calls at Ilkeston and Langley Mill. That would massively boost connectivity between the South Yorkshire and East Midlands main urban areas. It would also provide a second Sheffield station which some services could be diverted to and additonal services could use to places like Worksop or possibly even London/Birmingham. Yes its not ideal having multiple stations but Chesterfield provides a good interchange to the wider rail network.
Stocksbridge is a pretty small settlement all things considered. I am sceptical that one train an hour or similar is ever going to be able to generate sufficient traffic to justify the expense of reopening it, especially if it is not even coupled to the primary interchange stations for South Yorkshire (which I'd argue are Sheffield Midland and Meadowhall).
A stopping train on the line via Barrow Hill is going to be rather slow, with the number of stations that are proposed on it. Given the line is already apparently slower than the main route (both based on realtime trains an the fact that it is not the main route!), I am not sure how attractive a train from the East Midlands to Sheffield that is slower and also doesn't go to the same Sheffield station that almost all the other trains go to would be.
I would like to propose a thought experiment. Suppose Sheffield Victoria station's location had been lost to history, would people propose a station on that site as a "second station" for Sheffield today?
And I completely agree with this too. Leeds-Birmingham has to be the priority for the next TRU style upgrade, especially since the loss of HS2. The line has too many short restrictions in speed on what is otherwise a relatively fast line. The curves at Moorthorpe and Rotherham Masborough as well as the speed restriction at Burton Station need to be designed out. Increased capacity through select areas of three/four tracking should be developed to reduce interaction between intercity and local trains. Significant remodelling of Sheffield and re-signalling will also be required.
By all means try to implement some short term measures but we, as a country, should be looking to spend billions to improve connections between four major urban conurbations. Once TRU is finished, Leeds to Birmingham starts to look very poor compared to every other railway betwen relatively close major conurbations.
After TRU, if you want to improve Leeds to Birmingham I think your best option is likely to run a Birmingham Curzon Street-Leeds train via Manchester. It would seem to leave any reasonable upgrade of the classic line via Sheffield for dead.
I think a light rail solution, both for any future reopenings and for dealing with current congestion, would be the best option. It offers additional capacity at comparatively low cost and risk, and builds upon the experience of the tram train project. Let's say we did Stocksbridge and extended onto the Penistone line, that saves at least one path on the Sheffield northern throat alongside all the cited advantages for a return to rail-based travel to Stocksbridge.
