The premise that "information gathering" is a manager's most important task is a pretty interesting assumption underlying this post.
I recommend reading Andy's book "High Output Management" for more insight into this assumption.
Essentially a leader is not defined by your ability in doing something, it's defined by how well you are able to utilize your team's ability to achieve something that can't be done by one person.
An analogy to this could be having a chat box available on your website (olark for example). Let your users know you're always free for an informal chat.