There is a difference between the irresistible impulse, and the impulse not resisted. And that is why the best thieves don't get caught.
The offender must be able to give something back. But criminals are most often poor people. They have nothing to give. The answers to this are many. It is correct that our prisons are by and large filled with poor people. We let the poor pay with the only commodity that is close to being equally distributed in society: time.