The split ticket is cheaper than a through ticket
a) Because it is
b) Because you're limiting your available routes, for example you may have been able to take a more indirect route that would have been more expensive with split tickets with a through ticket.
Each possible journey has one or more 'flows'. Most only have one, 'Any permitted', but some have others, for example Leeds to Blackpool North has 'route via Burnley' and 'Route any permitted'. Each of these flows has a 'lead operator' who sets the interavailable fare. Once this fare is set, all other train companies on the route must accept it. Competing operators can create their own flow, like with Manchester to Stoke, the any permitted flow is set by Crosscountry, and Virgin Trains have set up in competition a cheaper, Virgin Trains only ticket. But Virgin Trains still must accept Crosscountry's tickets. Crosscountry aren't allowed to create a Crosscountry only flow as they are the lead operator and setting both interavailable and 'competitive' ticket prices would be a conflict of interest. On my earlier example, the lead operator for Leeds to Blackpool North any permitted is Transpennine Express, and for via Burnley is Northern Rail.
The lead operator is generally the operator with either the most commercial interest in the given flow, this does not always mean that they are the operator who takes the most revenue from it though.
Many fares are subject to regulation too, the train companies can't just charge whatever they want, they have to, on average, put these fares up by a maximum of RPI+X%. This year X was 1, due to coalition cutbacks to subsidies it will be 3 next year. Any individual fare may go up by 5% above RPI+X,as long as other fares are increased by less/lowered to compensate.
The protected fares are standard class season tickets, off peak returns created before about 2003, or where an off peak return didn't exist at this time, the anytime day single and return.
