According to studies and surveys, "breaking news" breaking news attracts more viewers and/or attention. That is understandable to a point. We are surrounded by the news since there are so many sources and types of information available nowadays. According to the same study, the majority of viewers of newscasts, for instance, are already familiar with 80% or more of the news being covered. In news, there is nothing "new." The tune-out effect then enters the picture.
The issue is that the word "breaking news" is being used far too frequently and without sufficient justification that it is starting to lose its meaning, as your inquiry implies.