There are plenty of ways to increase capacity on a railway line especially if you can build new rails, but at some point it just gets too difficult. The railways are surrounded on all sides, almost everywhere, by urban development. Homes and businesses have to be relocated, earthworks have to be done, and it all has to be broken into tiny pieces done in 4-5 hour spans in the middle of the night or over Christmas, because the railway is live and too economically important to shut down for long periods of time. Doing any kind of upgrades at all on a live line is horrifingly expensive and slow. That's why HS2 is a completely new railway. The UK has reached the limit of adding capacity to the West Coast Main Line; further upgrades are possible in theory but can't solve the fundamental issue of the same rails being shared by fast and slow trains.
As for Beeching, it's not quite that simple. The roughly 25-35% of the country that's pretty left wing hate the Beeching cuts for the same reasons they hate all government cuts.
Despite my negative view on trains above, I'm actually a train enthusiast. I love taking the train. I love reading about how they work. There was a story on HN some days ago where a rail engineer talked in detail about how the high-speed rail record was set, I absolutely loved reading about it. My girlfriend had to tear me away from the screen. And I've often wondered about how to really scale up the railways in a big way.
In a way, railways are kind of the ultimate nerd dream. An ideal railway is a huge, smoothly operating and very safe high performance machine, entirely coordinated by engineers and planners. I think perhaps that's why it's such a political hot-button issue: a nationalised railway represents a very tangible instance of massive state planning and control. Decentralising it is difficult for various logistical and technical reasons, not only the politics of it.
Despite that the Beeching cuts have never been rolled back, even under the 3 terms of Labour government. Many of those lines made no sense, especially in the context of continually declining ridership and the ever rising traffic on the roads. It'd have been a very irrational government that continued ploughing money into rail instead of building motorways given the expressed preferences of the population at the time.
For unknown reasons that are still debated today (but which align perfectly with privatisation), the decades-long decline in train usage reversed and so now new lines are needed again. But they're different routes to the ones closed by Beeching. Those were mostly small rural lines.