This is an imminently sensible idea - unfortunately, the system administrators at the university do not have control over individual PCs owned and "administered" by students and staff.
With the profusion of virii, worms and trojans, they are a sitting duck for DDoS attacks with the subsequent costs in terms of disruption to academic work, network non-availability, bandwidth costs and potential for litigation.
When I was at school my local administrator used to run probing and port-scanning tools and would contact people who were running insecure machines - this is an alternative, but the speed with which the recent worms have spread could quite easily have brought down a network in that time period.