Exclusivity played a role in Facebook's focus, though it is debatable whether the amount/type of exclusivity was optimal. While we are quite certain that a Facebook which started out catering to the general public would have faltered like Myspace, we're not so certain about what would have happened if Facebook had been all-inclusive for every college from the get-go. It provided a valuable service to all college students, but some would argue it did not have to trickle down from the Ivy League schools to maintain its focus on serving the needs of its usergroup.
In terms of design and type of service, FB may have been able to capture the entire college market (or at least more of it) from the start. I remember by the time Facebook first reached Stanford, it had already developed some very broad niche-based features (now lost) including a status message that told you which dorm your friends were logged in from. This feature would have been great for all colleges, though it is understandable it would have taken more time to develop and map if Fb had involved more campuses. This leads one to think more about logistics and overhead; starting off with all colleges may have been a managerial nightmare for Zuckerberg, Saverin, Moskovitz, and Hughes. Server costs and marketing would have been prohibitive, and small mistakes (service outages) could have had larger repercussions on FB's reputation.
So did exclusivity provide any added value on top of the logistical ability to focus?
The thought experiment to approach this subsequent question would be to ask: Had Facebook started off with all colleges and a more exclusive competitor (say, exclusive to Harvard - Winkelvoss et al's ConnectU for example) emerged, who would have come out on top and why? Did students at other colleges feel they needed to be as cool as Harvard students (or wanted to be cool by connecting with them?), adding value to the initial exclusivity? Did Harvard student membership add value to Facebook just as celebrity membership added value to Twitter? One might argue that to some degree, this kind of inferiority complex - for better or for worse - pervades all of society, but it is very difficult to measure and talk about!
Another relevant question would be how easy is it for you to transition from your exclusive usergroup to other usergroups? Are there conflicting interests?