I agree that a Sheffield - Buxton service would be useful but unfortunately as you said the infrastructure wouldn't permit it, going off topic slightly wasn't there reports about having the line being reopened between Buxton and Matlock funded by a cement company???
The re-opening of the line from Rowsley to Great Rocks has been debated extensively. IIRC - The last major exercise was in 2004 under the auspices of Derbyshire County Council.
https://www.derbyshire.gov.uk/site-...xecutive-summary-of-the-feasibility-study.pdf
I attended various sessions relating to this and many of the ideas proposed above were made then.
The basic conclusion was that:
"There are no insurmountable engineering difficulties in constructing a railway along the former corridor between Matlock and the existing Buxton to Chinley freight line at Blackwell Mill. However, a number of bridges will require to be replaced and a short section of new railway is required to pass around a gas regulator that has been constructed south of Rowsley.
Achieving a new station at Buxton, to suit the through route to Matlock, will, however, be difficult due to geometric, topographic and land use constraints. Two potential solutions have been identified including the continued use of the existing station (requiring trains to reverse direction). Neither are ideal. The more expensive option has been used in economic assessments of the project.
Significantly different levels of railway infrastructure are required to support the different options of rail service frequency.
Considerable work would be required to upgrade the existing freight-only route from Peak Forest to Chinley and this remains a key risk in using that route for new rail services".
As with many such schemes little was heard of this again until as you say a proposal from a tentative consortium of IIRC Peak Rail and a number of Aggregate and Cement companies suggested reviving the route. A key obstacle is the intransigent opposition of the owner of Haddon Hall, through whose grounds the line passed in a tunnel with cosmetic extensions at both ends to conceal the passage of trains. The removal of the bridge over the A6 at Rowsley further complicated the issue.
Since then there have been a number of successful initiatives to reopen similar lines – for example the first phases of the Borders and East West links, the success of which might encourage re-evaluation. There would need to be a lot of boxes to tick:
1: Harmonising a heavy rail route with the public access route through from Bakewell to Blackwell Mill
2: Establishing a pragmatic working relationship with Peak Rail who have made substantial investments in terms of both time and money establishing their project from Matlock to Darley Dale
3: Re-establishing infrastructure, in particular, in Buxton where the former alignment at the Midland station has been subsumed into the Spring Gardens Bypass. The former Station Yard at the North Western Station was converted into a bottling plant for Buxton for Buxton Water for many years until they relocated to larger premises on the outskirts of town. The site is now to be redeveloped for new medical facilities for the area. Various solutions have been proposed in the past including relocating Buxton Station to old Midland Railway Station Master’s House at the point where the railway crosses Fairfield Road – allowing further redevelopment of the existing LNWR station site..
4: Redoubling and resignalling the existing freight railways from Peak Forest to Buxton and Blackwell Mill.
5: Reconciling the objectives of stakeholders – the industrial interests are by and large catered for by existing arrangements and whilst they would be pleased to use any new facility that reduces their cost of delivery to destinations in the south may not be prepared to pay for an “all bells and whistles” reinvestment for other stake holders.
6:Passenger groups would undoubtedly like a revival of passenger links from Buxton to Matlock and beyond, together with links from Buxton to Sheffield but as has been stated track capacity through Derby has changed, the Hope Valley route is now the single Manchester to Sheffield corridor and the Midland Main Line and the Erewash Valley line is about to undergo radical change.
Whilst it is relatively easy to assemble a basket of synergies whereby if everything happened then there might be a project – there is the question of is there a “controlling mind” willing to put this all together? Derbyshire is a member for Transport for the North largely as a result of the vestigial links in the north of the county. There is also a combined programme with Derby City and Nottingham City and Shire concerning developments consequent on HS2. Whether any of these organisations would drive through a “doable” case with the DfT is at this point moot.