Research method is central in social science and indeed in any field of study. However, the appropriateness or centrality of any method depends on the type of research you are conducting. If for instance, you are carrying out an exploratory study, interview will be appropriate. Interview mixed with some quantitative methods may also be appropriate in evaluative studies.
It is difficult to know whether interview is central to your study without the knowledge of the details of the study. It is important however, to stress that method is central to any research. The degree of centrality of any method or methods is a function of the type and objectives of the research.
Within quantitative research, the most common alternatives are surveys and experimental designs, where the second option is both more specialized and more difficult to accomplish.
Within qualitative research, the most common alternatives are open-ended interviews and participant observation, where the latter is again more difficult to accomplish.
So, the popularity of interviews reflects not just their potential within both qualitative and quantitative methods but also the limitations of the most likely alternative methods.