My understanding is that the point of the Big Five model is that the design was the other way around—we started by looking at how answers to personality-related

My understanding is that the point of the Big Five model is that the design was the other way around—we started by looking at how answers to personality-related questions naturally clustered, then we gave names to those clusters. We define "agreeableness" because a particular set of answers/preferences/etc were correlated and could be interpreted as "agreeableness". Of course, there are limitations to this kind of approach and there's been a lot of research and refining done on top of this—not being an expert, I'm not familiar with it—but the core of the Big Five model is observational, not tautological.