The problem is the Leeds to Sheffield part of the service, not how it fits into the MML timetable. Leeds station is incredibly constrained, and the line between Leeds and Moorthorpe is incredibly constrained, so it's very likely that the only way to make those work is with a 6-minute turnaround at Leeds, regardless of what happens south of Sheffield.
You can sort of see how it would vaguely work it's just very resource inefficient. Currently you have one of the EMRs from London terminating at Sheffield at around xx42 (it moves by a minute or two depending on the exact service). There's then the fast Northern from Sheffield is at xx52 (again minor variation here and there). So plugging those paths together isn't particularly tricky. For the return leg there's an EMR back to St Pancras from Sheffield at xx35 and the Northern fast path from Leeds arrives at xx31 (again odd minute or two difference) so it wouldn't be particularly tricky to plug those together either.
The issue is those six minute turn arounds at Leeds which are wholly unsuitable for a long distance service both from a reliability perspective but also just cleaning/restocking it before sending it south again.
The only solution to that (without recasting the whole Leeds timetable to try and make this fit) would be for in effect each service to be a step back to the next service so the unit from London that arrives in Leeds at say 1238 would instead form the 1345. But a) there ain't no way your finding a through platform that you can occupy for that long at Leeds, b) if you want a bay platform instead (which you might find, maybe if you're lucky) you've got to ladder over a lot more of the alignment than you do for the current platform 12 arrangement, and c) it's a horrendous use of a precious unit it twiddle it's thumbs (or I guess auto-couplers?) for an hour.
I think it's a nice idea to have Leeds with additional links to places like Derby and new links to somewhere like Leicester as well as another direct London service. Plus you can see how it would work because there is actually a way of lumping existing services together to make it work (in theory, I feel like I might have someone like
@Bald Rick looming threateningly over my shoulder for lumping services together like this and going "Ta da! It works!"
).
But just from a resource perspective it doesn't seem like the juice is going to be worth the squeeze. How do you make the case for the extra 810s that would been needed to let them spend 2.5hrs+ going from Sheffield to Leeds and back (which is what would happen without a recast of the timetable to find a way of giving them a better turn around at Leeds)? Right now they spend 20/30 minutes in Sheffield and go straight back down the MML, i.e. on their core stomping ground.
Nice idea but I reckon the practicalities just make it impossible.
