It's interesting to consider the difference between categorization by tagging within a single Stack Exchange site, and the shunting of questions into the various subsites. Is the form of a menagerie of sites of greater value to the Stack Exchange network, or to users of the sites?
A Venn diagram including stackoverflow, programmers, ux, dba, cs, cstheory, security, codereview, and a few others, has substantial areas of intersection. There are over 37,000 stackoverflow questions tagged "database"; surely an exhaustive search for answers to some database-related questions would include both stackoverflow and dba. (Do answers from smaller SE subsites appear lower in Google search results?)
What if SE explicitly worked with a graph whose nodes are all the SE sites, their tags, their questions, and their answers? When seeking answers to questions, we don't care which site we find them on, so why not turn the SE browsing experience into one that can cross site boundaries? As far as I can tell, currently the only explicit edges among such inter-site nodes are the "this question migrated from site x" notices. The danger of the dilution of the SE network into something like Quora would be mitigated by the fact that there would be very few edges connecting bits of sites like stackoverflow and diy.
Surely there's value in seeing how data at the various sites are interrelated, mining those Venn diagram overlaps.
Tangentially, it's evident from the gripes here and elsewhere that there is substantial value in many of the "closed" questions. Instead of closing questions, perhaps they could be routed to some sort of alternate track, usenet alt-hierarchy-style. These questions would still be participants in the overall SE graph; let the user make an affirmative decision to opt in to the "alt" portion of the graph as part of their registered-user SE experience.
Prior awareness of how one's question would be categorized with respect to all the relevant stackexchange subsites falls into the realm of "don't make me think".