Here are the GWR stations officially designated as "request stops"
32926 UMB Umberleigh
28130 EXN Exton
21442 LEL Lelant
19666 COP Copplestone
17844 YEO Yeoford
17286 DMH Dilton Marsh
14116 MRD Morchard Road
7884 YET Yetminster
5844 SAR St Andrews Road
5782 KGN Kings Nympton
5684 DOC Dockyard (Devonport)
4972 BGL Bugle
3788 ROC Roche
2844 THO Thornford
2814 NTC Newton St Cyres
2720 CNO Chetnole
2538 MEN Menheniot
1906 LAP Lapford
1894 SCR St Columb Road
1494 LUX Luxulyan
1382 CAU Causeland
1330 SDP Sandplace
1116 SKN St Keyne Wishing Well Halt
496 PMA Portsmouth Arms
194 CPN Chapelton (Devon)
And they represent an interesting bunch. Perhaps the only commonality is that a significant proportion of trains that are shown in the timetable as (possibly) stopping there would not drop or pick anyone at all up if they actually did all come to a halt and let the doors open.
On a low speed line, in a line section where there's just one of these stations, for the stations towards the top of the list above where virtually everything calls, there's going to be little point in looking to putting in some extra system over and above a hand signal - you won't reliably speed the train up anyway.
Looking at Lochluichart (where we started) - it has a brother at Achanalt and a cousin at Achnashellach each of which has less that 1000 passenger journeys per annum. The line is laid for good speed (so a significant penalty is incurred in slowing down and speeding up) ans perhaps only 1 train in 20 calls at Lochluichart, 1 in 12 at Achanalt and 1 in 8 at Achnashellach. By slowing down but not stopping, you are perhaps saving 2 minutes each, and if you didn't have to slow down you could save 4 or 5 minutes instead. Change of making all the calls - unlikely, and the timetable from Dingwall to Kyle of Lochalsh could perhaps have 10 minutes clipped off train timings - especially in the knowledge that even if all three stop are made and the train's a bit late, there's good turn around times at the end anyway.
No accident that I posted in "Heart of Wessex". Thornford, Chetnole and Yetminster are not as rarely used as Lochluichart, common to stop at one of them or perhaps two. But all six (three on the way down and 3 on the way back) on a circuit is pretty unlikely, and if you can trim a few minutes off timetable you can get a clock face hourly service, passing at either Dorchester West and Yeovil, or at Maiden Newton and Castle Cary. Which being clock face lets you extend an hourly Bristol Metro trains all the way to Weymouth.
Of course, with the service up to hourly, would passenger number at the halts grow to the same extent as traffic on the line as a whole, or would the proportion of trains calling be reduced?
On other lines such as the Barnstaple, could you usefully move to an "Any train can stop anywhere" model and allow for - say - 20% of calls to be made in the timings?
5 calls not only suggests about 5 minutes required, but also gives 5 opportunities for the message to be lost, delayed, misrouted, misunderstood or otherwise fail to have the desired result ...
Perhaps my cynicism at the practicality was obscured by how I wrote it up. Almost as bad as getting a rail replacement taxi at Trowbridge on a Saturday evening ...