The main issue that, in steam days, led to stopping at Salisbury was the LSWR didn't have any water troughs (possibly because they didn't have any adequate level sections for them). As a result Waterloo, or Exeter, to Salisbury was as far as you could go on a tank of water. The LSWR and successors did have some notably large tenders for the size of loco. Because they would take a considerable time to refill it was the practice to change locos instead, which was invariably done - by maximising the water capacity the coal capacity was somewhat reduced as well. Waterloo to Salisbury and back was also a good days' work anyway.
This water issue, indirectly, is what led to the Ocean Liner Express crash at Salisbury in 1906. The Up express from Plymouth (actually from Devonport, where it reversed coming up the spur from the shipping terminal) couldn't make it all the way over all the gradients etc through to Salisbury on one tank of water, and they didn't want to stop twice, so the changeover loco at Salisbury was sent down to Templecombe, 35 miles west, which is about halfway between Plymouth and Waterloo, and changed there, thence coming through Salisbury nonstop. Apparently it was the Salisbury driver's first ever run through the station without stopping. Thereafter it was determined that the Ocean trains, at the time the only ones to pass Salisbury nonstop, would stop there, now having already done so at Exeter as well. Apparently there had been multiple prior instructions from management to Salisbury crews not to run through the station too fast with these trains, there had been concerns before the accident.
In the 1950s on summer Saturdays there was congestion at the station with all the loco changing, the main expresses being duplicated or triplicated at short headways, so the Atlantic Coast Express, nominally nonstop through to Devon, passed nonstop and changed locos at Wilton, next station west, the Salisbury loco again having been sent down there ahead. It did so while the relief, running behind, changed locos at Salisbury station.
Back to the original post about the Waterloo indicator showing Page 2 etc, this is just bad programming, where it fills up page 1, if there is anything left over (sometimes just one line) it then does a page 2, which looks silly. It should really be divided into logical sections, now with space for a more prominent text about it being continued.