In a real application you'd probably have some user accounts of some sort that are stored in a relational database already and then you'd suddenly have to scan for events in a directory that you then have to connect to those records in the database.
So there might be some specific set of applications where you are right, but there are specific things that a database is really good at, which would make it a really good choice. With the proper indices you'd probably get the same or even better throughputs, unless you come up with some clever directory structure for your events, which would in fact be the same as an index and only on one dimension whereas in a database you'd be able to create indices for many dimensions and combinations of dimensions.
So you are right, trade offs.