PRIV only gives discounts on Anytime fares. This means it is cheaper to use Advance for long distance journeys.
For medium distance journeys where flexibility is required, then splitting is the best option but the splits are often at different places to where a non-PRIV holder would split, e.g. for York to Birmingham day return, a PRIV holder would get York-Donny, Donny-Tutbury & Hatton, Derby-Birmingham. But a non-PRIV holder would get York-Sheffield, Derbyshire Wayfarer, Burton-Birmingham. However a Y-P holder would get York-Sheffield, Sheffield-Derby, Derby-Birmingham.
Our fares system is designed to penalise people for travelling longer distance journeys, compared to people who only travel short or medium distance journeys by charging them more than the sum of the individual journeys. However when breaking it down into chunks to avoid being ripped-off, you have to vary the place where you split depending on various factors. If you don't have a degree in railway ticketing then you run the risk of being effectively defrauded by the TOCs.