If 24/7 availability is required, the company should simply hire someone to work those hours, perhaps in a different timezone if needed. Many mistakes are going to be the result of management pressures to "ship" too quickly, incentivizing cutting corners, which someone will have to deal with at some point, even if it's during their regular working hours.

Nah, the rota is large enough that it will likely be somebody else’s problem anyway and the chances are even if it does land on them they just won’t answer the phone.

Punishing mistakes with unpaid overtime has never been a good approach to quality. It just teaches management that they can get away with low quality because the engineers will pick up the pieces in their own time.