Library listservs can be great for keeping up with the goings-on in the professional world or sharing problems and concerns with your colleagues. Some are very low-traffic, while some send several hundred email messages a day.
However... If you can't manage the amount of email you get, maybe you should UNSUBSCRIBE from some of those lists. If you can manage to filter listserv messages into folders, or get digests instead of individual emails from the list, GREAT! But if you are unable to read work-related emails because you "just get too many emails to read them all," then get off the lists. That excuse is insulting, and it says a lot about your skills as "an information professional."
Also, if you spend more office hours sending and responding to listserv messages than you do working at your real job, maybe you're not as necessary as you think you are.