There are all sorts of different reasons why lines and stations might have escaped closure in the 1960s where others that were ostensibly similar got the chop:
- A common one was where the line was still needed for freight, so there were fewer savings to be made from nixing the passenger service if all the track maintenance and signallers etc were still going to have to be paid for anyway.
- In some rural areas, the difficulty of serving the communities by road meant that the railway was retained – the Tamar Valley and Esk Valley lines are good examples of this, where some of the villages on the Tamar Valley line are separated from Plymouth by wide river estuaries that have no road crossings, and the narrow, winding and hilly roads in the Esk Valley regularly succumbed to snow (this was a bigger problem in the 1960s than it is now)
- Keeping smaller station calls on a 40mph branch line costs a lot less (time, money and passenger goodwill) than keeping the same stop on a 100mph mainline
- In the specific case of Battersby, because trains need to reverse there, the time lost by having a station stop is basically zero. The alternatives would have been (a) building a new curve, which was implausible in the 1960s were new infrastructure for minor branch lines was definitely not on the cards, or (2) retaining the line west from Battersby to join the mainline at Picton, missing out Great Ayton, Nunthorpe and other intermediate stations to Middlesbrough and putting the train on a circuitous route that would likely have taken longer than the reversal.
The main reason that the Esk Valley line is slower than the bus for end-to-end journeys is because it takes a meandering route and has a linespeed of mostly 45mph or less.
You make it sound as though Northern are only serving these stations out of some kind of misplaced loyalty to small villages or because it hasn't occurred to them not to ... they
have to keep these stations open under the terms of their contract with DfT! The likelihood of any putative potential passenger growth from cutting out these intermediate stops outweighing the number of passengers who use those stations is small.
What do you think an open access operator would be able to do on a line like the Esk Valley?
Making quiet stations into request stops isn't always a viable solution. While it can save a little bit of money by not stopping, and can potentially save a little bit of time if you can reasonably assume that every train will be able to miss at least a certain number of stations, there are sometimes complications around sightlines. I know there is/was at least one station (I think in Wales) that was a request stop in one direction and a regular stop in the other, because in
that direction there was too little visibility of the platform from an approaching train (and likewise too little visibility of an approaching train from the platform).