Efficient use of stock could be enforced by auctioning diagrams (so if you want to run the 0700 LIV - 0900 EUS for the business traffic, you're also obliged to operate the return working 0930 EUS - 1130 LIV, 1200 LIV - 1400 EUS and so on*) - but that would mean that timetabling was done by whoever ringmastered the whole show - presumably the government. And that wouldn't go down too well with 'small government' wonks, or lead to a timetable that was particularly responsive to passenger demand.
*Yes, a two hour journey time and thirty minute turnarounds at the terminals. It makes the sums easy, and you can always dream.
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Actually, it seems to me that if you lose the concept of open tickets, and don't worry too much about government involvement, this could be made to work (although making something work isn't the same as coming up with an optimal solution).
To try and work a simple example, let's imagine a Y shaped railway system - a very simplified WCML with trains up the leg of the Y from Euston to Stafford, and Liverpool at the end of one arm, and Manchester at the end of the other. London (Euston), Manchester, Liverpool (Merseyside) and Staffordshire all have public transport authorities (PTAs) who are required to (and are to some extent funded to) consider long distance travel for their residents. The public transport authorities are all responsible to the public in the same way that TfL, TfGM and Merseytravel are in the real world.
To make auctioning work, there must be a vendor with something to auction. Let's call that the DfT. Based on something - the existing timetable? Pure guesswork? - they prepare a timetable and put the lots up for auction.
The bidders bid. Some lots are sold. Some aren't. The DfT has a look at the timetable that is produced. The DfT will then conduct another auction - but with a different set of bidders. The public transport authorities are asked to bid to have services operated in the vacant slots that haven't already been filled commercially. The authorities (we imagine) will do what is best for the community they serve, and make their educated judgement of how much money they should commit to serving their community So Merseytravel may be prepared to pay £5,000 for a train from Liverpool arriving at Euston at 1030 - but if TfGM is willing to pay £5,500 for a train occupying that slot south from Stafford then Manchester will get an extra slot at Liverpool's expense. Staffordshire County Transport (SCT) will presumably not care where a train has started, as long as it goes to Euston, but happily bid £1,000 for a train arriving at Euston at 1030. They might also want to bid £2,000 for a train to Liverpool but not want to offer so many opportunities to Manchester so only bid £1,500 for a Manchester train. But if TfL had wanted a train to Manchester only a little more than a train to Liverpool, and so had bid £3,250 to Manchester but £3,000 to Liverpool, we find that the total bid for the train to Liverpool is (£3,000 (TfL) + £2,000 (SCT) = £5,000) while the total bid for a Manchester train is (£3,250 (TfL) + £1,500 (SCT) = £4,750). Liverpool gets the extra slot.
So, two auctions have been conducted. The train companies have bid for the trains they want to run. In the gaps this has left, the PTAs have put money into the pot for the trains that they would like but which the train companies don't want to run. We must therefore open a third auction: the train companies will bid again on the services that the PTAs want to run, in the knowledge that they are bidding to be given the money that the PTAs have already put in.
It would work. But even on my Y-shaped system, it's complex - and not necessarily transparent. But if Virgin (or whoever) insist, it can be made to work.
