The points you raise would make sense if cats were purely logical, unfortunately they're not and a lot of what makes a cat work is instinct.
- Instinctively, cats will hunt.
- Lack of care about food source will make cats outlast prey who have to leave safe areas to find food.
- Lack of care about food availability can (and has been proven to) cause cats to hunt more often, not less- as the "cost" of going for a hunt is basically zero; there's no consequences for failure and even success is met with satisfaction but no "cost".
- Instinctively, cats will hunt.
- Lack of care about food source will make cats outlast prey who have to leave safe areas to find food.
- Lack of care about food availability can (and has been proven to) cause cats to hunt more often, not less- as the "cost" of going for a hunt is basically zero; there's no consequences for failure and even success is met with satisfaction but no "cost".
Anyway,there's better info on this subject: https://en.wikipedia.org/wiki/Cat_predation_on_wildlife