Carrying on from Sheffield to Leeds does not sound like a good idea, not sure when they stopped but back in the day a few St Pancras - Sheffield HST services used to carry on to Leeds, and on the one occassion when I used it was very quiet. I dont think passenger volumes would justify it today either.
For through passengers from London the time penalty would rule it out, of the main stops on MML London Sheffield services the only one which currently doesn't have a through service to Leeds provided by XC is Leicester. (I can understand people not wanting to use XC but thats a different issue)
What would make sense would be to try and sort the timetable out so that the connection is maintained under normal circumstances.
One of the reasons people want through trains from everywhere to everywhere is the dire state of connections generally, with connecting services being despatched even if the feeder train is in sight and pulling in and bad experiences when connections are missed. The silo mentality between the various ToCs just adds to it.
Other countries seem to be able to make connections work, so its proven to be possible. I realise that unless the service is a self contained branch line indefinite waits for a delayed incoming service are not possible, but a level of common sense would not go amiss.