People in the north Lakes tend to gravitate towards Glasgow or Edinburgh for their nearest "big city", and people from the south Lakes tend to gravitate towards Manchester. Whilst many in the north Lakes would also go to Newcastle, York would not really be on the radar.
The Tyne Valley Line is busy on the peak flows to and from Newcastle, but during the rest of the day the line tends to be quiet. So quiet, in fact, that Northern have introduced Advance tickets for £4 each way to try and encourage more off-peak usage. The daytime trains stop only at Haltwhistle, Hexham and the MetroCentre and do the journey in about 1h20. IMHO they should also stop at Haydon Bridge, which normally generates a big crowd on the 685 service bus, but they don't. The hourly Northern service is perfectly sufficient for the market.
Many people do drive, but that's because they're already in their cars having come from places like Caldbeck or Keswick. The A69 is slower than the train- if you can average 50mph on the single carriageway section you're doing well- but people drive because it's easier than trying to park at Carlisle station. Carlisle city itself is small and impoverished and always has been.
There's no need for shunting, the westbound platform at Hexham is bi-directional with a crossover to the east of the station. The shunt in the morning is only required to get the 2x142s out of the way of the following Newcastle to Glasgow train. During the day the Hexham "shorts" arrive and depart from the westbound platform.
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Even longer on a 142, which is what it was usually booked for!