However the train did not stop in the midlands, and I think this is the important thing. It only ever really served Leicester
Its a problem of how to "serve" the East Midlands with any proposed Manchester service.
At the moment only Nottingham has a direct service (some Regional Railways "Cross Country*" services from Manchester used to run via Loughborough - Leicester - Melton Mowbray to get to Peterborough instead of the current "Grantham" route, but this was dropped along with places like Blackpool/ Ipswich). Can't remember the timings, but going back to the Leicester route would keep the 90mph 158s off the 125mph ECML between Grantham and Peterborough.
Running a Manchester - Derby - Leicester service like you propose would tick two boxes, but may mean cutting the existing Manchester - Nottingham link (since there are better things that could be done with its paths, like Manchester - Sheffield - Hull and Nottingham - Sheffield - Leeds).
One alternative for CP6 may be wiring the Uttoxeter line and providing a Manchester - Stoke - Derby - Nottingham EMU - even with the speed of the current Northern stopper to Stoke and EMT Sprinter to Derby, it can be comparable in journey times with the Sheffield route - even more so if 100mph EMUs could be sourced instead of the 90mph EMUs/ 75mph DMUs on the two legs).
The five thousand people of Bakewell may not agree, of course.
(* - not to be confused with XC - this was the precursor to the current EMT Liverpool - Norwich service - it used to have more variety of route/ destinations)