Thank you all for your input in answering the question.
I'll accept my naivety
and leave the running of the railway to those who know what they are doing.
I think it's a perfectly reasonable question that you've asked - there's certainly a common refrain amongst enthusiasts along the lines of "privatisation has pushed up costs by requiring all of these pen pushers, and we could save a lot of money if only they were abolished", but the number of staff involved is pretty small compared to the overall railway and the work done is intended to save the railway money (by identifying where problems actually occur and assessing whether the costs involved justify resolving them).
For example, the only late service at Sheffield recently was the Liverpool - Norwich train - a long distance route with reliability issues that will soon be chopped at Nottingham -
https://www.realtimetrains.co.uk/train/W88354/2020-08-25/detailed - it was on time leaving Lime Street at 10:51 and survived Castlefield unscathed to be on time at Chinley (as it approaches the tunnel that takes it under the Pennines/ Peak District).
It was scheduled to get into Grantham at 14:05, at which point the 90mph 158 (which might be substituted for or include a 75mph 153/156) has to find a path on the fast ECML to Peterborough - if it can't get to Grantham in time then it might be waiting for a while to join the busy ECML (obviously things are a bit thinned out at the moment). So if the service arrived in Norwich late enough that compensation was due to passengers, where would the blame lie? Was it due to Network Rail infrastructure (signalling, tracks, engineering)? Due to train staff decisions? Passenger at fault? Badly maintained train? Waiting on another service? (I can't see that there was a delayed train ahead of it, but that's often the case in the Hope Valley).
How do we stop this happening again? If a dodgy signal at Chinley (*) causes hundreds of pounds of "delay repayment" for passengers at Norwich then I understand that the cost would be allocated to Network Rail, and they'd then have to assess whether the cost of improving/replacing this signal was good value for money compared to the cost that they were shelling out to inconvenienced passengers.
* - I'm making an assumption here - it could be that the fault lay with another TOC/FOC or with EMR themselves - e.g. if the reliability problems of their 1980s train is causing them thousands of pounds in compensation then that's an incentive to improve their maintenance to minimise similar issues in future - if a badly pathed freight train or an unreliable Northern stopper is at fault then the cost should be apportioned there for them to shape up.
I think that the important thing to remember is that this kind of "attribution" happens at all large companies - public sector too - if you nationalise the railways then you'd still have people trying to assess root causes, since it matters if you want to improve things - e.g. if weak electrification is costing millions of pounds of delays then you'd need to know those costs to compare to the bill for fixing the problem. This wouldn't go away under any kind of "New British Rail" (it happened under the old British Rail too) - if you want to run things better then you need to know the root cause of what is currently going wrong.