Not at first, but good torturers work through using questioning techniques to find out the most horrible thing to do or say. And they enjoy that work. Someone with empathy wouldn’t be able to go through any of that. Unless the end goal was to improve this situation for the subject. Ironically, the method for both of these is cognitive and behavioral psychology.
You’re correct in your initial assertion, but you are incorrect in your assumption of the overall methodology (and goals) for either, or both.
Edit: the short answer is that none of this is as simple as you think it is, and you can actually do some pretty simple research into this and find out a lot more than maybe you wanna know. Extending a little on that, it actually gets pretty fucking ugly especially when you get into with the Nazis and the KGB did towards the end of World War II and going into the Cold War. And the United States government did some pretty ugly stuff as well leading into the 50s and 60s and 70s. Don’t get me started on what the bush administration was doing.
You can look into interrogation techniques and some other stuff about how we ended up figuring out that rapport building and not torturing people as a much better way to get information out of them. I’m preferred, myself, while I was studying for a masters degree in psychology to stick to the much lighter side of stuff, and how that type of psychology can be used to help and heal people Instead of breaking their brains open for tiny bits of information that mostly turned out not to be very useful anyway. 
Not at first, but good torturers work through using questioning techniques to find out the most horrible thing to do or say. And they enjoy that work. Someone with empathy wouldn’t be able to go through any of that. Unless the end goal was to improve this situation for the subject. Ironically, the method for both of these is cognitive and behavioral psychology.
You’re correct in your initial assertion, but you are incorrect in your assumption of the overall methodology (and goals) for either, or both.
Edit: the short answer is that none of this is as simple as you think it is, and you can actually do some pretty simple research into this and find out a lot more than maybe you wanna know. Extending a little on that, it actually gets pretty fucking ugly especially when you get into with the Nazis and the KGB did towards the end of World War II and going into the Cold War. And the United States government did some pretty ugly stuff as well leading into the 50s and 60s and 70s. Don’t get me started on what the bush administration was doing.
You can look into interrogation techniques and some other stuff about how we ended up figuring out that rapport building and not torturing people as a much better way to get information out of them. I’m preferred, myself, while I was studying for a masters degree in psychology to stick to the much lighter side of stuff, and how that type of psychology can be used to help and heal people Instead of breaking their brains open for tiny bits of information that mostly turned out not to be very useful anyway.