Yes, a good speaker will be reasonably competent with all types of music. But, depending on a speakers strengths and weaknesses, some kinds of music may be a bit favored or disfavored by a particular speaker. For example, the Zu Audio speakers are extremely dynamic sounding with the ability to deliver extremely sharp-edged attack to the notes. They sound very fast and lively with demanding electronic/dance music. But, that comes with a rough, peaky sound (prominent upper midrange and high end) that might not be so objectionable for that kind of music, but it may be less loved playing acoustic music.
Every speaker has its strengths and sometimes that strength is anathema to some other quality. The only way to get around this is to have multiple systems (isn't that a dream?).