I would imagine police forces would be even more short staffed if officers were never allowed any time off. No one would join. Then we'd all have to look for our own motorbikes, and deal with our own RTAs.
Does anyone honestly think that people work more efficiently if they don't have holidays and days off? Why should the police be treated differently from anyone else who works.
And in fact as is turns out, even when not on duty they all 'worked' by helping in an accident. Risking injury or even death to help the driver. I wonder if they demanded overtime for the time spent helping those people? - I doubt it.