A few miles to the south (and it is not far away) the old LSWR Exeter line was treated differently. Although in old days its expresses also ran nonstop from Salisbury to Exeter, or only served middle-of-nowhere Yeovil Junction, when the expresses were withdrawn, along with the lesser basket case intermediate halts, a useful intermediate service on the line, serving the nowadays 12 intermediate points, sprang up.
Indeed. Due to the previous emphasis on express services, the most important intermediate stops had been the junctions e.g. Templecombe and Sidmouth Junction (now Feniton). Honiton and Gillingham were largely ignored. Once the branch lines were closed along with many of the junctions (although Feniton reopened in 1971 and Templecombe in 1983), the pecking order of the intermediate stations rapidly changed. Gillingham and Honiton are two of the three busiest between Exeter - Salisbury along with Axminster.
Gerry Fiennes's book 'I Tried to Run a Railway' indicates the aspiration had been to only leave Honiton, Axminster, Crewkerne, Sherborne (railhead for Yeovil, as Yeovil Junction isn't in Yeovil anyway) and Gillingham open so that the intermediate service was pretty fast in its own right. He wasn't happy that so many other intermediate stations remained.
Exeter - Taunton was also heavily rationalised, with Cullompton and Wellington losing their services. The ongoing saga of whether they are to reopen highlights the basic problem - you either need to slow down intercity services to call there, or you need to run local services which don't get in the way of expresses. It's worth pointing out that this is a 30 mile two track 100mph railway with fewer than 3 passenger tph and very little freight most of the day in 2019 - there are plenty of 125mph sections of the GWML or ECML which would seemingly be trickier to timetable.
One interesting proposal which never happened was the retention of the Heart of Wessex, but with closure of all intermediate stations between Frome and Weymouth (possibly not Yeovil Pen Mill, but definitely Dorchester West). Apparently the line was seen as an important Channel Island link at the time which could prosper despite the decimation of local traffic. As it is many stations closed, but Chetnole and Thornford survived despite being concrete platforms in the middle of fields.
It always surprised me that none of the Tarka line stations were closed despite the fact it was earmarked for retention. It's hard to see there being much outcry if Portsmouth Arms or Chapelton had closed.