And... you'd need a database to track the databases!
Actually, as I think about it, separating databases really just becomes semantics. As long as it is a single application, separating the databases adds overhead (mostly for the developers) but in reality, it is always still all one datastore. One way or another, the application has to behave essentially the same no matter which way you do it.
The one advantage to having them separate is that you can have different "versions" for different customers. But I'm not sure that that is a good thing.