I think closing stations on an otherwise open line is an easier sell than closing an entire line. If line closures are unacceptable/political suicide then surely the next step is to see how costs could be reduced. Should we be looking at light weight tram/trains (diesel/battery?) for lightly used branches, with much reduced signalling etc. operating more like a tram, with track brakes and more or less line of sight operation, but able to operate over a normal lines to reach a junction station.
I've certainly wondered about this myself. There aren't actually that many wholly or nearly self contained branches, but I do think this idea has potential for those that are, e.g. Cornish and Thames Valley branches. There are lots of costs it saves:
1. Level crossings can be open with normal traffic lights (the tram just stops before crossing, or runs at a speed where they could stop if a car jumps it)
2. No lifts needed - just walk (or wheel your chair) across the line on the level; the tram is driven so it can stop if you're in the way
3. If done low-floor like Sheffield, new stations in more useful places cheaper and easier to add or move (branch stations are often poorly located)
4. Staff can be cheaper than mainline staff if operated as a separate organisation - I believe Metrolink tram drivers are far cheaper than train drivers
5. DOO is the norm, or if conductors are used they don't need to get involved in operations and can do all your ticketing - low or zero evasion, no TVMs or booking offices to pay for, and people actually like it!
6. Potential for street running at the terminus if it's awkwardly out of town, or diverting through a town in the manner of Oldham if the station is inconveniently sited
Etc.
Plus I'll add my usual bugbear - better bus integration!
Also there must be an option for a simpler signalling tech like RETB on single track lines (double track you can, as suggested, just operate on sight, potentially with road-vehicle-derived radar anti collision technology as a backup).
With regard to closing stations, there are some that do get in the way of a neat or improved service - I've mentioned New Lane, Bescar Lane and Hoscar as ones which if removed could allow for a fully regular interval service on the Southport line, and usage of all of them is extremely low. I'm not sure closing them is worthwhile if they neither get in the way nor cost very much though - for instance there's little point getting rid of Berney Arms unless that whole line closed (which it could, I suppose, but when I've suggested it I've been told there are capacity issues on the other one), but if you look at e.g. the Far North some pruning of the more pointless ones could allow a speed-up which would improve the line's economics by attracting more users - or the Marston Vale where exactly that has been proposed.
I think it's also worth looking at how people get to such stations and ensuring that rather than just binning it off, genuine consideration is given to how those people who do travel might. I've suggested for one that an acceptable substitute for Aspley Guise station in the 5-station option could be a cycle and footpath alongside the line connecting it to one or both of the nearest alternatives, as the road routes round are rather hilly and long. This might even be relevant for higher-use stations which are annoying to operation of the service - for instance, does everyone* who uses Cheddington arrive by car? If so, would they all be willing to drive to Tring or Leighton Buzzard? If so, is the station worth retaining? That is, in some ways it matters less if people use a station and more if they'd be really easily persuaded to use a different one. This will be more the case for stations for longer journeys - I think for instance if you closed Aughton Park there's a good chance a lot of journeys would simply be lost to the car entirely.
Or can a station be made viable by a large housing estate being thrown up around it? (I don't know if Cheddington is green belt, but there'll be ones where it could). Should the railway perhaps promote this? It has done before - Metroland - and it hugely does in Japan.
It is genuinely possible for closing things to result in better transport outcomes
if done correctly. Beeching mostly failed to do this (though the idea of regular interval, frequent InterCity services was one positive outcome). I fear we can't manage to do that, but we should.
* OK, there are about 6 houses right next to it, but they don't justify it on their own.