I think it might be worth noting at this point, that whilst TOCs are responsible for the disciplining of staff and the actual fares they set, the guideline, or instruction, to offer only through tickets actually comes from the Ticketing and Settlement Agreement (TSA), which is something the DfT insists TOCs keep to, and the TSA has been in place since Privatisation first came about. In fact I would think the advent of cheaper advance purchase tickets under BR would have made splits a possibility back then.
Also it might be worth considering that some people (even on this forum) consider that TOCs talking to each other about fares pricing would amount to price fixing, this limits how much can be done to limit splits, given the framework we have thanks to, yes you guessed it, the TSA.
Oh and, to end, some TOCs, Northern being one, continually look to remove these anomalies where they can, however some splits are caused by PTE area fares, which is a complex mess to solve.