I’m not sure that it is. It is indeed tricky — risky even — but I think the potential payoff of such a project outweighs its considerable pitfalls.
I’ll restrict myself to two points, one methodological and the other more substantive. First, a point on historical method:
I grant it is very important not to confuse actor’s and analyst’s categories when doing history. It would be a grave error to import our modern notions about the relationship between biology and the public into a discussion about 16th century natural history, thinking they apply in roughly the same way. However, that does not mean we cannot use modern concepts as a useful analytic jumping off point for a historically sophisticated conversation.
One way we might do so would be to trace a constellation of modern categories backwards in time, watching them coalesce into older concepts, disciplines, and ways of life. Having done so, in our case it it would then be important to realize that early modern natural history has a number of descendants besides contemporary biology. (Including popular institutions like zoos, acquaria, nature documentaries, etc.) Moreover, as we trace the path of natural history to modern biology forwards in time again, it’s equally important to take note of the many cultural and intellectual influences that creep in laterally, as it were. (One obvious source would be medicine, but there are many others.)
Historical genealogy is difficult, to be sure, but that does not mean we should shy away from it at the get go!
The second point I want to make is more substantive. Tracing the historical relationship between biology (or science more generally) and the public is extremely important. One reason is precisely because in so doing we learn how difficult it is to make this distinction before the late 18th or early 19th century. However, we also learn that issues of community membership are always being negotiated along some register or another. Moreover, I do think we can say that an important shift took place around the turn of the 19th century. As disciplines like biology coalesced into coherent and powerful social institutions, their practitioners deliberately went about setting themselves apart from other sectors of society. I would argue that it is certainly worthwhile to investigate their reasons for doing so, as well as the mechanisms by which they succeeded in policing the epistemic boundaries that signal their status as holders of expertise.