Based on the pre-Covid timetable, Sheffield had four/ hour to Barnsley, a reasonable split of departure times, a mixture of two “fast” (stopping at Meadowhall only) and two “slow” - it worked really well, pretty much turn up and go for the bigger stations
There were generally five/ hour from Sheffield to both Doncaster and Chesterfield (four/ hour to Derby made up of three of the trains that stopped at Chesterfield plus one non-stop XC), but the long distance trains had paths determined by bottle necks elsewhere and so were very badly spaced (whilst you might hope that the Doncaster services had a good split between the two “semi fast” trains - Hull/ Cleethorpes - and the two stoppers, I think that four of the Donny services were in the first half of the hour, with just one train expected to mop up demand in the other thirty minutes)
Same with the MML to the south, the half hourly EMT/EMR to London and half hourly XC towards Birmingham both departed around xx:25/ xx:55 each hour, so the four/ hour to Derby was pretty lop sided, the Chesterfield services were a little better (they included the hourly EMT/EMR service to Norwich and the hourly Northern stopper to Nottingham) but still two of the five were around xx:55
So, being selfish, you could have used the same number of trains/paths to provide a much better split of departures to/ from Sheffield. However the services are relatively long distance and involve a lot of carefully pathed sections (New Street, the two single track sections between Hazel Grove and Heeley, lack of grade separation at intermediate junctions especially at both ends of the Rotherham “loop”, various conflicts with slow moving/ randomly timed freight), so I don’t think you’ll ever be able to provide a well balanced timetable on these busy lines. Maybe it’d be Possible to run an extra local shuttle to fill certain gaps, but I don’t think that Sheffield’s cramped Station could cope with many more.
Frustrating!