I don't think "narrow minded" has to be something negative. I would say my mom is narrow minded with music, she listens to a very limited list of 70's and 80's hard rock/heavy metal/rock bands, but she would be the first to agree with me if I said that. It's not like being open minded and enjoying every genre is superior to having a specific taste and preferring your music to be in certain ways. I can get frustrated when people showcase narrow mindedness, but if they like their limits and listen to the kind of music they like, then that's really all that matters.
As for how it plays into this debate, it depends on what qualifications you want to judge a singer on. A singer having a range that expands into harsh vocals, even if you don't like it, is still showcasing something. It's like talking about who is the best film director. While I don't think so personally, a lot of people would say Spielberg is the best, because he has done great movies in so many different "styles". War movie, sci-fi, action, adventure, comedy, horror, and so on. If you make 5 masterpiece movies across 5 completely different genres, does that make you a better director than someone who has 5 masterpiece movies within the same genre? Some would argue that the variety and range makes the first director superior, but others who mainly watch movies in the genre by the other director would say otherwise. Just a silly comparison, I'm tired.