Despite the regular assertion here, I can find nothing in the Ticketing & Settlement Agreement that prevents a ticket office offering split tickets, even without being explicitly requested.
Of course, TfW or any other TOC are at liberty to instruct their staff not to offer splits unless requested. (But FWIW, I was at a TfW station yesterday and the ticket office staff volunteered that a split might be relevant for the journey I was making!)
It's implied within the "Impartial Retailing" section (6-30) of Volume 1 of the TSA (starting on page 170 of the PDF), rather than explicitly stated. The requirement not to offer split tickets unless a specific combination is explicitly requested comes from Knowledgebase (and the National Fares Manuals before it). One reason for that being that you might offer a split at X on a journey from A to B, but it may actually be cheaper to split at Y and Z, so you've still not sold the cheapest ticket.
Ticketing and Settlement Agreement said:
An Operator which Sells Fares, or provides information about them, on a train or at an Impartial Point of Sale or an Impartial Information Centre must act fairly and impartially between Operators. Any such information that is provided must be factual, accurate and impartial.
Let's say, for example, that you're working at the Ticket Office at Sheffield and someone asks you for a Day Return to Birmingham, travelling on a weekday at around 09:45. The only ticket you can sell that complies with impartiality rules is the Off-Peak Return (priced by XC) at £52.80.
That you can bring that down to £33.70 by selling an Off-Peak Day Return to Derby (priced by EMR, and costing £13.30) and an Off-Peak Return onwards to Birmingham (priced by XC, and costing £20.40) is irrelevant
unless explicitly requested, as proactively offering the split breaches the impartiality rule (given it directly affects XC's revenue).
The TSA continues:
Where an Operator is asked to recommend a suitable Fare..., it must request sufficient additional information to enable it to make the recommendation.
If more than one Fare is suitable, the Operator must explain the main features of the alternatives in an impartial manner.
And finally, Section 6-31:
MATCHING OF FARES TO PRODUCE A THROUGH JOURNEY
Where, at an Impartial Point of Sale, a person indicates that he wishes to make a journey for which a Fare is not available, the Operator which operates that Impartial Point of Sale must offer to Sell him a combination of two or more of the Fares offered for Sale at that Impartial Point of Sale which between them are valid for the whole journey unless such a combination is not possible using the Fares that are offered for Sale there. The Operator must use its reasonable endeavours to ensure that the combined Fares meet the Purchaser's requirements.
Given through fares are available for the vast majority of journeys on the network, it's rare that the clause in question will need to be invoked, but when it is the Seller needs to make sure they comply with relevant rules regarding use of a combination of tickets.
YMMV when interpreting the section in question, of course.