And where a train that is reasonably not PF (say points NW of Skipton) comes into an area that has PFs?
That specific train is non-PF throughout, as doing otherwise would be confusing - that is (was) the Swiss model. You would need to have enough staff on board to ensure that all tickets were checked.
Alternatively you could have a train that was PF for part of its journey, again indicated clearly on all publicity, but the train would have to wait at the "boundary" station until the guard had been through to ensure everyone had a ticket before entering the PF zone, which is just a bit complex.
Perhaps it was not such a good idea that the railway historically branded many of these services as Paytrains.
It was an excellent idea, and it provided the kind of consistency and simplicity that I think is needed. It fell down by requiring rebooking at the connecting station, but that was only due to the technology of the day and needn't be the case now.