I've used this service a few times each year since before privatisation, and by observation the DfT conclusion that there isn't a significant demand for this service to operate through Nottingham is correct; there have nearly always been some passengers who remain on the train, but never many. Moreover, when looking at unoccupied reserved seats, I can't ever remember seeing any marked for journeys between Manchester/Stockport and places east of Nottingham.
Pre-privatisation, BR used to close the Erewash Valley line for maintenance on summer Sundays, and between Chesterfield and Dore on winter Sundays (think that's the right way round!); Manchester - Norwich trains therefore passed through Derby on summer Sundays, and I joined them there on a number of occassions, and from memory there often seemed to be others who'd joined at Derby making the same cross-Nottingham transfer. In more recent times, I've also seen passengers making the Nottingham transfer at the same time as me, and therefore I'm not surprised that Abellio are proposing to extend the truncated Norwich - Liverpool service to Derby; there are insufficient to make the extension viable in its own right, but the provision of another service in the Derby - Nottingham corridor is to be welcomed (there are 'Red Arrow' express buses between the two cities every ten minutes and typically nine stopping ones each way every hour, so there must be a significant demand which - hopefully - rail can capitalise upon)