I suppose my theory on whether medium- or long-distance links should have been kept open is: 'if there is a green-signed trunk road [the A6 in this case], there's demand for a through rail route'. Not saying this theory is correct though.
Could tourism have also been a factor in keeping this route alive, with the 'right' service (i.e. a limited-stop service from the cities as suggested above) given it goes right through the Peak District? I still maintain that part of the reason these lines were unprofitable was that they had a poor service - Oxford to Bletchley is perhaps a striking example of this. The theory is "make the service good, and people will use it" - which has been proven in recent times on Chiltern for example, but was not a popular theory at the time of Beeching.
But in 1967, where would these extra passengers come from? Making what kind of journeys? Oxford-Bletchley trains, running about every 2-3 hours were running seriously under utilised and making a massive loss. Doubling the service would have doubled the operating costs. Would it seriously have doubled the number of passengers? And even if it did, the line would still be making a loss.
In a way British Railways did follow your theory - consolidate the available passengers onto the minimum of lines (recognising that those not catered for were going to be lost, but they could not be catered for economically anyway) and then increase frequencies on those lines remaining. But real success had to wait until social changes put more money into peoples' pockets and increased leisure travel, and also made people less residentially mobile, thereby increasing longer distance commuting.
Prior to the Beeching period passenger numbers were on a downward trajectory on most lines. There was very little evidence that increased service would result in sufficient extra business to turn loss making lines into a profit. Where it had been tried (Bristol suburban for example) they had often not produced worthwhile increases in passengers to pay for the additional costs. What manager would have staked his career on doing just that between Oxford and Bletchley at that time? None.
The last few posts, including this one, have hit the nail on the head for something that I find a bit frustrating in these "We should have kept..." conversations. There simply weren't that many trains around then and the lines were often able to survive because of the needs of freight. Marylebone never had much more than about an hourly service, half of which didn't get beyond Rugby, so the idea that the GC was this hugely busy mainline is just wrong. There were about as many trains from Marylebone to Manchester in a day as there are now from Euston in an hour or so! RT4038's reply at post #116 details six trains a day from Leicester to Manchester but two didn't come from London and one was a sleeper. Talk of a missing link for Leicester to Manchester is perfectly sensible but these days people would assume a frequent service would be needed, say hourly, not a small number daily. The destinations of interest would be swamped with trains, so the modern way is to have some through services and some connections.
An hourly frequency out of Marylebone onto the Great Central proper [i.e. beyond Quainton Rd] is a little overegging things, and no train terminated from the south at Rugby Central! In Summer '56, the departures on Mo-Fr were 7.47am (to Leicester, stopping), 10am (to Manchester, express), 10.20am (to Brackley, stopping), 11.55am (to Manchester, express), 1.30pm (to Woodford, stopping), 3.20pm (to Manchester, express), 4.50pm (to Bradford, express), 5pm (to Woodford, stopping), 6.12pm (to Woodford, stopping), 6.18pm (to Sheffield, express), 10pm (to Manchester, express).
I am not sure where forum posters think all the resources would have come from to increase services to hourly clock face headways? The railways were virtually bankrupt - increasing services double (or more) in the hopes of gaining enough extra business to produce profits would just be laughed at - perhaps some key inter city routes, but certainly not bucolic byways. Quite rightly too.