If you're only using one dish, then sure it's probably better to wash by hand. No one I know has ever suggested running a dishwasher for one dish.

Dishwashers can handle a lot of dishes and loading them takes like five minutes. Yes, it might take between 2 and 3 hours to finish washing, but it's asynchronous, you're not involved with the process. I usually load and start the dishwasher right before I go to bed.

This is not even to mention the fact that many dishwashers can sanitize dishes better than you can by hand since they can get very hot and maintain that heat, and the fact that they use considerably less water.