... should be banned.

JK.

We all have our personal reason for staying invisible. But I think it would be better if mods don't use the invisible mode.

Well...we can get list of all moderators from "Forum Leaders" page and regular members know who is more frequent and whom to PM for a problem.
But for new members it may not be easy. A new member may request "Admin" to move a thread or something....And during some time in a day no mods/admins are visible in "Who is online" list.

Not that anyone complained me....just saying 'cause I've faced similar problem in some oher forum.