I've been talking this whole time on this blog about an individual's personal research activities. The contradiction here is that we belong to departments, to teams, yet our research challenges and accomplishments pertain to us individually. It's always my work.
In the typical Research I institution, the faculty do not duplicate one another's interests. For example, we have, in Peninsular Literature in my department, one medievalist, two early modernists (one specializing in Jesuits, the inquisition, and narrative prose, the other on theater), one 19th century specialist (working on theater and illustrated periodicals), two 20th / 21st century scholars, myself (working on poetry and poetics, translation theory), and Jorge, who works on contemporary narrative, film, and culture. My colleagues are very smart people, and they are good to have around if I have questions to ask about their fields, but we don't really collaborate on research. My interests are closer to those of our specialist in Latin American poetry, with whom I've co-taught a course, but generally those who share my particular interests live thousands of miles away.
The NRC ratings of PhD programs came out recently and my department is ranked fairly high in some categories. We are definitely a top 20 Spanish department. But what does that mean if we are only the sum of individual achievements?
There might be other models. For example, you could organize a department as a team devoted to a particular area. To study Latin American poetry, you could have a department that just did that, with everyone stepping on one another's toes and jealous of one another's accomplishments. Hierarchies would be even stronger than in normal departments. Students who decided they weren't interested in that after all would be kind of stuck. Undergraduates wouldn't have a lot of course offerings.
In geographically more compact areas (not Kansas), you could have research groups linking members of several universities. With the internet, you can collaborate with far-flung scholars. I'm always looking for other models to get myself out of that purely individualistic mode.