Yes you can. Easily. I looked at the graph today. It’s 12 mins running time for an electric LNER train non stop, and 21 for a DMU stopping at all intermediate stations. The long distance services are flighted within approx 20 minutes northbound and 30 mins southbound. Granted the local trains wouldn’t be at exactly 30 minute intervals, and there might need to be some long layovers round on the branch, but it would still be 2 tph. It would be even easier if every other local didn’t stop at Manors (given the Metro is next door) and all were EMUs. The reason it has not been done is that no one is willing to pay the extra subsidy.
Well you can take my word for it - your neighbours either haven’t been building new railway bridges for a while, or have the wrong rate books. Or both.
A standard ramped footbridge now costs the thick end of £2m. The road over rail bridge at Ufton Nervet was £7m - in the easiest of open country with a land owner (the sitting MP) who was willing to sell and therefore no need for a Transport & Works Order or Compulsory purchase. That was 3 years ago.
A simple footbridge, required to carry a footpath used by less than 5 people on most days, at Hathersage was costed at £750,000 at the time of the public inquiry in 2016. It won't be built before 2021 by which time I doubt it will cost less. The cost of consultations and public inquiries in both time and money needs to be factored in.
The Selby diversion was largely driven by the need to develop the short lived Selby coalfield. It runs across totally flat countryside. Any Morpeth diversion would require cuttings and embankments as well as several road and foot bridges and a viaduct across a deep wooded and picturesque valley. To be of most benefit the new curve would need to be gentle, possibly starting north of Pegswood, but either side of Hepscott could be difficult.
All of which explains why it hasn't been done before. It's not as if it hasn't been considered - can't recall exactly when, probably after one or more of the crashes. Morpeth Station is being, maybe now has been, improved to offer better facilties.
If track congestion is the issue, providing a passing loop or two at about £10m a time might be better value. Depending on topography it could be less or more, but consultations may mean every one of them might take 5-10 years from now to achieve.