Car pooling is a big win. Universities should encourage it. Primary obstacle is probably perceptions of safety.
Well, instead you might incentiveise it through having car pool car parks that are closer to campus, or at least next to a well lit and preferably sheltered area. Then you could publicise the car pool scheme. You could even have a forum for finding other car poopers, and/or an app. Maybe allow people, with their consent, to be matched by approx origin/destination for easier finding.
If you had a computer science or math department then I'm sure they would have people who could solve the ride matching problem.
Given that there often is a bus or even many buses, the question then might turn to "Why do people prefer their cars to a bus?". And now we're back at the beginning.
The disconnectedness of suburbia is at the heart of this, but essentially insoluble in the short term.