One thing that crossed my mind, given that Keynsham station buildings were demolished in the 1970s, was perhaps doing the same thing at St Annes Park and Saltford didn't stack up financially.
The point I was making in my earlier reference to
The Development of the Major Railway Trunk Routes is that 'stacking up financially' was not the point; it was all about closing anything you could get away with. Stopping trains on trunk routes, then as now, were considered a nuisance. What better way of getting rid of this nuisance than by closing intermediate stations?
As I never actually used Oldfield Park until about 10 years ago (it was simply a station that trains stopped at that I was travelling on before that) I don't know whether any demolitions took place there, but I am sure there is someone on this forum who could tell us about that.
A quick look on Wikipedia reveals that:
There was originally a full-time station master and ticket office. The 1929 ticket office was constructed of timber on tall wooden piles attached to both the Brook Road bridge and the ground below. It was located at the Moorland Road side of the bridge at road level. This has now been replaced by a portacabin styled ticket office on the westbound platform and a ticket dispensing machine.