Whimple, Feniton and Tisbury are a major reason why a lack of gangways would be problematic for a replacement - they all have short platforms. Whilst guards on the line are proactive in informing intending users to be in the front 3 coaches, making sure everyone has moved before Cranbrook / Honiton and Gillingham / Salisbury is likely to be very challenging and will inevitably fall short on occasion - most likely due to passengers not paying attention, but this is still something which can be avoided with gangways.
There are no barriers anywhere between Exeter Central and Salisbury so revenue duties are important. No end gangways wouldn't help.
You could get around these issues by having the successors to the 159s be 5 and 10 coach trains with SDO, so Exeter-Salisbury stations are served by trains of a uniform length. Most of the day 5 carriages might only be excessive between Axminster and Yeovil Junction, which is only a quarter of the distance between Exeter and Salisbury. No end gangways should then be fine.
The other option of course is that you withdraw the through service into London and run it as a connection instead. GWR have just done exactly that for Bedwyn.
There are sizable numbers of passengers for London from all stations between Yeovil Junction and Salisbury - I'd be very surprised if that wasn't the primary destination.
The total passenger usage for Kintbury, Hungerford and Bedwyn pre-Covid in 2018-19 is given as just over 500,000. The total passenger usage for Tisbury, Gillingham, Templecombe, Sherborne and Yeovil Junction for the same period is over 1.1 million, with Gillingham alone used by almost 400,000. These places are also considerably further out of London and haven't got the fastest service to begin with, but it's still well-used. As trains have always gone through to London Waterloo in normal times, even during the grimmest years for the route between 1967-1980, running a shuttle and forcing a change of train would not be popular to say the least.
In any case, the only logical place to run a shuttle to would be Basingstoke. Salisbury is still off the juice so no benefit splitting there unless you use battery trains, which will immediately lead to the question of why they aren't being run over the whole route. Basingstoke is pretty busy most of the day and having one platform constantly blocked with shuttles to Exeter and Salisbury, which will also require low speed manoeuvres on and off the fast lines west of the station, isn't going to help operationally.