The problem with what you are looking for is that you are looking for something that is really approaching the same general field of work from two entirely different philosophies addressing two different phases of the processes. The word processor and page layout applications, such as Word and InDesign, revolve around the fashioning of a single document with a high degree of typographic and layout control. What exports from them should be, or at least can be, ready to take to the press. At that point of the game, the notion of having lots of smaller files making up a bigger file would be a strange way to go about things (you could argue that linked media lives in that realm, but that is fundamentally different than text). On the other hand you have a relatively new breed of application (at least compared to the document processing genre) which is aimed right at the author and deliberately eschews extensive formatting on the premise that such is a hindrance to the creative process at that stage. These applications, which Scrivener falls within, are basically not book generating platforms, they are content generating platforms. There is an important distinction there. Some go so far as to not even allow any formatting at all. Scrivener lets you use some standard formatting controls as this is more natural for the majority of authors not accustomed to marking things up with symbols. But that doesn’t mean it should be confused with book generating software. 
It is still very much content generating software. LaTeX is really the only notable exception to this in both Scrivener and Ulysses—and even then I bet hardly anyone just exports to LaTeX and runs straight to the press with their PDF. That will get you 95% of the way there, whereas working through a word processor is probably more like 80%. Neither is 100% print ready in the majority of cases.
So on the other side of the issue, are the types of project management features and multi-file outlines seen in applications for authors, useful in a word processor or layout engine? I don’t think so, because at that point word flow becomes integral with page flow. It suddenly matters what page text is on. Thus adding or subtracting words in a long stream provides immediate feedback toward this fact. You can see, right in front of your eyes, that if you add a paragraph in front of a figure, you might be pushing another paragraph meant to address that figure onto the next page. You might decide that is okay, but the point is you get that feedback immediately. If there were somehow multiple files feeding into this long text stream (something that would very weird to implement and work with, I think), you’d lose the immediacy and “presentation first” aspect of these programs which is, by definition, their entire point.
Therefore, you don’t really have anything that does both. It’s two different problems, both quite complex, and it would take extraordinary developmental resources to marry them—if such a marriage would even be wise in the first place. It would take a Microsoft or an Adobe to really address this thoroughly—and it would most likely have to come from that direction. The sciences of typography and layout are very intricate. Microsoft even screws them up on a regular basis, badly, and that’s considered to standard method of accomplishing these tasks in most contexts.
I think, to put it into perspective, a good analogy would be photo catalogue software and Photoshop. Both Apple and Adobe have taken a crack at combining these to a degree, in Aperture and Lightroom respectively. Neither does even a tenth of what Photoshop can do—and that’s probably a good thing. Organising images and providing near infinite pixel and vector level control over them are both very complex problems, better left discrete. Consider, even these two massive corporations have no intention of making a AperPhotoLightRoomShopeture. It would be a monster.
As Mark puts it, either way would be extremely bloated, and very likely a lopsided attempt where one part of the equation is deeply sacrificed for another. Your best bet will be to search for macros or plug-ins for existing word processors that increase its organisational capacity—but none of those are going to escape the single-document boundary—they will merely better the ability to manipulate a large text via some kind of outlining enhancement.
As an aside: Are you sure you mean BBEdit? That program is nothing at all like a word processor, or even something like Scrivener. It’s a plain-text, single-file editor. You can’t even make something bold in it.
