I don't think it helped that the service wasn't great, and had no pretentions to being InterCity or even 'Regional Express' from what I can make out. While it's a fair point that local journeys might be better served by buses, the route provided, potentially, an inter-city link between East Anglia and the West Country, as well as opening up connectivity to both Oxford and Cambridge from other parts of the country.
If someone had had the imagination to create say a two-hourly Cross-Country type service from Bristol to Norwich via Oxford and Cambridge, stopping only at the major towns (so something like Bath, Chippenham, Swindon, Oxford, Bletchley, Bedford, Cambridge, Ipswich (? - bit vague as to the geography of rail lines round here) and Norwich, for example, I'm sure it would have attracted passengers who wished to travel from west to east avoiding London - even if the small local stations had to be closed.
I don't think that this 'imagination' would ever have got off the drawing board. Anybody suggesting such a thing would have been laughed away, at that time.
British Railways were very short of cash at that time, and any available investment money would have been used in either (a) improving the speed and efficiency of the main Inter-City routes, or (b) reducing the costs, particularly that of labour [i.e. elimination of steam traction, manned level crossings, manual signalling etc]. This line had a large amount of manual level crossings between Oxford and Bedford, and was manually signalled throughout, except in the vicinity of Bletchley Station. Money going to upgrade these would have been money taken away from upgrading the core network. The line was operated by diesel multiple units. Running diesel multiple units from Bristol to Norwich would not have been an attractive proposition for passengers. Diesel locomotives would be more expensive to operate, and anyway were all required at that time for the elimination of steam traction, and diverting them away from this task would have financial repercussions elsewhere and unlikely to be agreed.
BR already had plenty of experience of long distance trains largely over the secondary network, and it wasn't good financially. (Midland & Great Northern, Midland & South Western Junction, Somerset & Dorset, York-Bournemouth via the Great Central and various others). The small number of passengers that would be attracted to such a service as you suggest would be more economically served by the Associated Motorways coach network, which catered for most of the flows.
There would have been a number of operational constraints - there was only one through platform (serving both directions) at Cambridge in those days, so capacity was tight for through trains. The trains would have had to cross the WCML on the flat at Bletchley. There would have been no interchange at Bedford (the stations are about a mile between each other, and the link lines, whilst in situ were not passenger lines, and only DMUs could have reversed in the south bay platforms of the then Midland Road station). The platforms at Sandy prevented the ECML from being four tracked at that point, which was required for capacity enhancement. All of these could have been resolved (indeed some are being now), but only by the application of large sums of money, which was simply not available.
Simply, the likely revenue from these trains would come nowhere near paying for the costs of running the line, and the investment required to reduce some of those costs was not justified to redirect it away from elsewhere on the network.
