I work at a commuter college (probably 80%+ students commute) with a vaccine mandate for everyone on campus, and we have a lot of students who live in multi-generational households, i.e. they live with their grandparents. Even though the risk to college students is relatively low, the decision to mandate the vaccine was as much (if not more) about mitigating spread to the broader community as it was to protect the direct campus community.
In short, the more people — big and small — who are vaccinated, the closer we are to herd immunity.