In my humble opinion, if your goal is to be the best, you will be successful. I am a strong believer in being specific in your offerings. Often, less is more. You can't be all things to all people. When you try o be all things to all people, you run the risk of becoming nothing special to anyone. Do one thing and do it better than anyone esle.
However, the more specific your offerings, the more population you need to support your business. In Manhattan, there is a pickle store. They only sell pickles and they sell a lot of them. This concept works in NY, but I wouldn't advise opening a pickle store in a smaller city.
If your city is big enough to support a small, specific menu, go for it. If are the best and put your heart into your business, people will come.