I sure hope that school does a first come/first served dorm choice. I definitely see your point about the principal.
UW-Madison has a housing lottery so a student applying late has just as good a chance at getting their top choice dorm as the early bird. U- Minn (with reciprocity with WI so similar pool of students) has the first come/first choice (or they did awhile back) so it paid to get the dorm deposit in earlier. I believe both schools did refunds up to a spring date. So- specifics matter.
In this era most UW freshmen will choose the public dorms (there are some private dorms close to campus) while most beyond that will go to apartments (small Greek numbers). Campus culture varies with schools. As do costs. In my day off campus mainly meant being further away, now there is a lot of private housing contiguous with one or another part of campus. But that decision comes after a student has been on campus for a time.