I completely agree with utilizing current technology such as a good CMS (be it WordPress, Drupal or something else) to project the public image of the school. For information that is parent or student specific, there are many ways to grant limited access via password and user settings, and in addition, for anything learning-related (that is, directly related to a class or curriculum, behaviour, attendance, etc), the school should be using an LMS to share this information over the internet.
As Shawn mentioned, teacher pages that are out of date and collecting dust should be shuttered. There are many services available online for teachers who wish to present a public portfolio, and the truly web-savvy can work with one of these or manage their own domain. For communication with students, the LMS or CMS can serve this purpose.
As with any company, a school should be concerned with its brand. A public school where student populations are more set and consistent can use their public online face to build community relationships and keep parents and neighbours abreast of ongoing events, be they sport, art, club or academic. A good community of support around the students can only enhance their experiences.
For other schools, such as universities and private institutions, the public webpage serves a purpose primarily as a marketing/student recruitment tool, secondarily as an information portal for existing parents and students, and also as a point of contact for staff recruitment. A quick glance at any well-constructed international school website will demonstrate all of these aspects, usually with a parent and student communication area behind a login screen.
Short of human resources and will, there are no reasons why schools at all levels can’t have a professional face to present the community. Where there is a lack of staff capability, there are student resources available as well as the associated learning opportunity that maintaining the school website can provide. Much like the student newspaper and yearbook, the calendar or event listings can be kept up to date; older students can produce videos and podcasts or other media for distribution, providing lessons not only in website management and development, but media, privacy, and responsible internet “face.”