That said I think the question must eventually come down to whether the bad things that happened to BR would have been able to happen to the Big Four if they had remained private companies.
There's no easy answer to that question IMO. Had nationalisation not taken place the Big Four would have been afflicted by most of the problems that beset BR in its first two decades, in terms of growing competition, falling traffic, outdated equipment and rising costs. Given that in 1946 shares in even the GWR were trading at half their value (and the LMS and LNER were in a worse position still) with little imminent prospect of improvement, they would have had great difficulties raising money to invest in modernising the system. It's very likely that there would have been major cuts in services and route mileage. That might have happened earlier and more gradually, and perhaps in a less arbitrary fashion than the Beeching closures, but it would still have happened IMO.
The managerial problems would have been rather different since had nationalisation not happened there'd have been no British Transport Commission to impose extra cost and bureaucracy. However, instead there would have been the old problems of co-ordination between companies, duplication of functions and lack of standardisation. Besides, as I said above, I can't see how the Big Four could have survived in their old form. They would have needed a subsidy at some point, and with that would have come some of the same difficulties that BR suffered in terms of prising money out of the Treasury and maintaining their independence.
One advantage to private railways would have been freedom to change routes. It's very doubtful the a Beeching Report could or would have been implemented across four separate companies, and the companies would have been able to build new lines to take haulage traffic. (Perhaps duplicating existing routes for this purpose.)
Also, they'd have been able to respond to growing towns and cities in a more flexible way. If they had withdrawn lines, they could have restored them far more rapidly than central government. Plenty of the Beeching lines can be restored, and need to be: the recent BBC4 season on the railways have a programme on Norfolk where the operator wouldn't restore lines because it lacked the power to do so (not owning infrastructure, which makes no sense).
This is possible, but it does rest on the assumption that, left in the private sector, the Big Four would have been solvent, well run, innovative and expansive. I have to say, I think that assumption owes rather too much to ideology. It's often been said that state-owned railways are inefficient, unresponsive to demand and slow to innovate, happy to manage a slowly declining railway rather than developing new business. Those charges have all been laid at BR's door, not without some truth. However, state-owned railways all over Europe have shown themselves capable of developing new services, seeking out new business and providing high-quality services. I have SNCF and the TGV in mind, but there are plenty of other examples. Meanwhile, privately owned railways in the United States wilted in the face of growing competition after the war and responded with retrenchment, disinvestment and cutbacks until Amtrak was created in 1971. I don't, therefore, believe that privately owned railways must always work better than state-owned ones.
The problem with this debate - in general, not specifically here - is that people tend to posit a rather idealised model of what privately owned railways could theoretically have achieved, and compare it against BR's poor early record. That's not invalid, but there's just as much scope for stressing that privatised railways don't have to run well and that the Big Four had flaws and weaknesses of their own and would have struggled in the post-war period, and for suggesting that had BR been structured differently (in particular, it should have been a stand-alone business rather than part of the BTC), managed more effectively and funded more consistently, it could have done much better than it did in its first two decades.
The Beeching cuts weren't only short-sighted and incompetent, at times they were absurd. Right now we have a few tiny hamlets with stations, while towns of 20,000 are miles from their nearest route. A private system could take the impetus in addressing this.
As I said above, I think cuts would have happened anyway, although the process might have been slower and more rational. One of the great absurdities of Beeching, of course, was the closure of the Oxford-Cambridge line, despite the fact that it ran right through an area whose population was expanding rapidly and passed close to the then-new city of Milton Keynes. But to be fair to BR, it did begin a limited programme of reopening lines and stations from the 1970s.
As for building completely new lines, I'm not at all convinced that a private railway system could do that much more effectively than a state-owned one. Again, I'd point to the impressive record of European railways on that score, and also Japanese National Railways prior to their privatisation in 1987. I can't offhand think of any privately-owned system that's shown itself to be nearly as expansive.
An alternative, however, is a series of regional "London Passenger Transport Boards". This could have real advantages, with latitude and non-profitability.
I'm not quite sure what you mean here. We already have some regional bodies - the Passenger Transport executives, set up under the Transport Act 1968 - which try to co-ordinate transport mainly in the major conurbations and have played a significant role in developing railways in one form or another. Greater Manchester PTE, for example, was largely responsible for developing the Manchester Metrolink light-rail network. The PTEs have been a great success and I do think there could be an expanded role for them in future.
Oh, and trivia question for railway buffs: when did "railroad" become exclusive to America? I know the Victorians used it, but it seems to have died out. Shame, I like it.
Good question! I don't know for certain, but 'railway' was pretty much universally used by the end of the nineteenth century and it was in common use from an early stage. The rail-connected dock that opened in Hull in 1846, for example, was called Railway Dock right from the start. The impression I get is that 'railroad' and 'railway' were used interchangeably early on, perhaps with 'railroad' slightly more common (certainly the word was used a lot in connection with the Rainhill Trials), but that 'railway' gradually became universal.