Just determining who the actual users of the system can answer some important questions about what the system will have to (or not have to) do. Finding out who else cares about what the system does, even if they will never use it directly, can also quickly identify important functionality. Very few systems are built to be independent of any existing systems these days, and interfacing with existing systems is often the source of many frustrating problems, so it is important to identify these systems early. What the client wants is important is, of course, important to you, but if what the client wants is different from what the users want, then you should know about it as soon as possible.
However:
Identifying actors takes time and effort, not only from modellers but also from stakeholders, and, of course, the actual users. Getting access to users can be difficult, especially if they are not employees of the stakeholders' institutions, and many actors will not relish being the objects of analysis. Modelling users can also irritate stakeholders if they don't consider users a high priority. They may much prefer their money was spent on something useful, like programming.