Speaking as someone outside the industry, the solution must be to recruit enough drivers so that running a full timetable is not dependent on rest-day working. But we know DfT and the TOCs don't want to pay for the extra training, along with increased pension commitments etc. Is that more or less correct?
It takes about a year to train a driver and 1-3 months to lose one.
The balkanisation of privatisation and the need for drivers to have competence on routes and traction means you have very small allocations of human resource that make it very difficult to forecast or resource changes hypothetically e.g. TPE at York vs LNER at York vs Northern at York.
It also means their competence largely mirrors the existing timetable and if TOCa varies their timetable or their rolling stock, a huge training requirement of hundreds and thousands of hours is dumped onto the roster.
In the BR model, a York driver might drive all of the routes and stock of the three depots above, larger depots sizes, more job variety, more flexibility and resilience.