I don't know if pacers are banned from Nottingham. I would have thought that they have just not been cleared south of Chesterfield. Even if they can't run down the Erewash mainline south of Chesterfield I am sure that it wouldn't be too difficult to clear them via Worksop and the Robin Hood Line.
I've been at Worksop, when Robin Hood Line trains have been late running, and they have arrived and departed from the same the platform, so it is possible to reverse there without using the reversing sidings.
A through service from Sheffield to Nottingham via this route would mainly benefit lots of passengers from stations north of Nottingham, especially the Mansfield area. Unless you are willing to endure a 45-50 minute wait at Worksop for a connection to Sheffield it is not very convenient to travel north from Mansfield without first going south to Nottingham. I am sure that Mansfield and the northern section of this line would see significant passenger growth with a faster service to Sheffield. Even just providing better connections at Worksop would be a help. No-one wants to make an almost 2 hour train journey, including wait at Worksop, for a journey that is only 45 minutes by road.
Incidently, as my local station is on the Robin Hood Line, I do not really want pacers, but would be willing to put up with them for local journeys if it helped EMT out of their stock problem and gave me a quick service convenient link to Sheffield.