I still believe that letting a cat do the work is much more humane than most other options mentioned here, such as poisons, the feeding of cement, or boiling alive. Not to mention once a cat kills one, or two most others will scurry away. Live traps would never catch enough in a timely enough manner and what are you going to do with the ones you catch? Turn them out to be a nuisance to someone else? Are you just going to give them the coop and move? You just have to pick the best option.
I've never seen a building that rats couldn't get into. It would have to be giant rats that couldn't find a way into a building. We have a barn with cement floors and tin outer walls they still managed to get in there. They could squeeze themselves flat and go under doors. I saw them climb up the wood heaters flue and squeeze out around it. We had quite a huge problem with them until we put the cat in there. Within a week you didn't see rats. He didn't kill all of them, they just decided to leave once they realized a predator was among them.
Of course everyone is entitled to their own methods of dealing with these pests!