The idea for re-opening the line has been around for decades, probably since the 1980s if not earlier. I don't think anyone has ever advocated a non-stop Derby - Manchester service - that wouldn't carry enough passengers. Any new service would surely include a 1 TPH semi-fast stopping at exactly the stations you mention, plus a 1 TPH 'all stations' - whatever they would be, north of Matlock.
I could see the merits in that arrangement - although seeing as it would only really be feasible to have 1 track with passing loops, it might be tricky to fit all that down there. The problem is that this risks becoming too much of a local line - neither the Buxton nor Matlock ends are fast, and so it would become a slow route that would be hard to market as an express - I can't imagine Derby - Manchester would sustain such a service, and it may not be the quickest option from either Notts or Leicester.