Building loyalty to increase usage and therefore increase revenue, obviously.
That is a somewhat pat response without considering who would GBR be keeping their customers loyal to, against what competition. The Tesco clubcard, for example, is designed to keep people shopping in Tesco, as opposed to their competitor supermarkets.
I doubt that the somewhat paltry rewards offered by the current schemes are enough to tempt anyone who is considering alternative modes of transport, such as car or coach. And the costs of a scheme that were to offer rewards significant enough to do so would be unaffordable.
The current loyalty schemes are largely designed to keep you buying from a particular TOC's website, rather than their competitor TOCs. Once they are all GBR, that competition has vanished.
I think that the LNER scheme, with it's discount offering, is also aimed at attracting customers away from the likes of Uber. But for the reasons explained previously, I cannot see such a scheme being rolled out across GBR.
I doubt that the current schemes attract much additional revenue, as the rewards for buying extra tickets are so paltry in comparison. The number of additional revenue journeys generated must surely be insignificant compared to the number of free and discounted journeys being given out as rewards. And I doubt that the Treasury would be willing to underwrite a scheme that increases usage on routes that are already deemed to be overloaded.
As I say, I really cannot see much incentive for GBR to offer a scheme.