The fundamental problem is that “rabbinics” implies both a body of literature and a distinctive methodology or approach to that literature. In some quarters in Israel this perhaps accurately describes, for good or bad, how rabbinic literature is studied (e.g., philologically in a “department” of Talmud). In the American academy, however, “rabbinics” is not a discipline. Those of us who primarily use rabbinic literature are situated in departments of religious studies (most frequently), language and culture, and history. We are scholars trained in a particular discipline who use rabbinic texts for our data. I do not “do rabbinics.” I “do” Jewish history in antiquity, using rabbinic texts as one (even if it is the primary) set of sources.I don't have a horse in this race: if specialists in "rabbinics" want to call it something else now, that's okay with me. But I do think that the field of the study of the rabbinic literature needs to be called something. Also, I think the death of "patristics" is somewhat exaggerated and, again, we need to be able to call the study of the corpus of church fathers something. I consider myself a specialist in (inter alia) "late antiquity," and I know very little indeed about "patristics," so I don't consider the former term a good replacement for the latter.
To put my point more broadly, it is a fine thing that older fields are increasingly embedded and cross-fertilized in a larger interdisciplinary framework (e.g., Jewish history in antiquity or the study of late antiquity). But the narrower disciplines still exist and still need to be called something. I work in both Jewish history in antiquity and in the study of late antiquity, but I do so drawing on, for example, Qumran studies and Pseudepigrapha studies (which are coherent fields in themselves—although some may disagree with me about Pseudepigrapha).
Let us indeed be clear what we are talking about, but this involves precision as well as synthesis. I am hesitant to abandon the older more precise terms until either they are replaced individually with something better defined or I am convinced of a cognitive gain in abandoning the precision they represent.
There is an important discussion to be had here.