You can't look at Beeching outside the context. And the context is given by the December 1960 White Paper "Reorganisation of the Nationalised Transport Undertakings". At that time, the operating loss of British Railways was some £60 million per year, with a further £75 million per year of interest charges making the total losses of British Railways some £135 million. And this at a time when a million pounds was real money - as a percentage of GDP, it's equivalent to £10.4 billion today.
To deal with this situation, the White Paper replaced the amorphous British Transport Commission, in which there was no real accountability against individual transport sectors, with the British Railways Board. This Board took on the assets of the railways and was solely responsible for the capital debts of the railways. It was this Board to which Richard Beeching was appointed in March 1961. One can see the 1960 White Paper as a prototype for Sectorisation 25 years later, in a way.
What's crucial is that the White Paper specified that "The practical test for the railways, as for other transport, is how far the users are prepared to pay economic prices for the services provided. Broadly, this will in the end settle the size and pattern of the railway system. It is already clear that the system must be made more compact. There must also be modernisation, not only of lay-out , equipment and operating methods, but of organisation and management structure."
In other words, the decision to cut the railway network was made four months before Beeching. The policy had substantial government support, and came from the viewpoint that the railway network could and should be made to pay by getting rid of the parts of the system that lost it money. After all, the nationalised transport industries were seen as profit-making industries first and foremost - nationalisation wasn't seen as a route to subsidies, but as a way of fairly distributing profits.
No contemporary government would have backed anything significantly different from the Beeching cuts; had Beeching, or someone else in his position, proposed a solution that didn't involve appreciable cuts (or one that required subsidy) then he would have been replaced. A more traditional railwayman might - and I stress might - even have been a poorer choice for the job, by attempting to cling to outmoded methods of operation (like pick-up goods trains) for too long.