The Southern were heavily represented on the Railway Executive who ran the railway in wartime, and it's said that when Didcot to Newbury was doubled first, and then on to Woodhay, first station down the Southampton line, the Southern stopped further progress because they didn't want a GWR double track line at Southampton ...
Regarding current travel patterns, there is maybe some demand from the area to Oxford, to Reading, and to London. Only the first would make any use of a Didcot-Newbury line, which were not through routed to Oxford, and would be difficult to compete with road travel on the parallel modernised A34. Few houses are walking distance from the old stations, so you would need to get the car out anyway. That sort of "against the grain" rail line just doesn't work nowadays.