Hi Max!! Welcome to the Blog.
I have periodically thought about starting a student running club, but never pursued it. I frequently run with colleagues, and usually very early in the morning (6ish). Our training schedule and student sleep schedules just don't mesh, so that has been the end of it. I will admit, I've also had some reluctance, even though it would be fun, for several reasons. The principle one is that it appears to create a form of access that is possibly gendered and certainly unavailable to many students. The second one is a fear of looking foolish: (1) because I am slow; and (2) because I look rather ridiculous in running shorts (just ask Spencer). The third is that I have a big mouth, and it becomes bigger when I run (just ask Spencer).
The one time I have run with students is during the annual Race Judicata. This is a race organized by our Student Bar Association in honor of a former colleague. I run it whenever I can, and also offer to pay an extra dollar to the charity for each student who beats me. That always turns out to be a great day. So, maybe I should just get over my reluctance . . .