We have several former student reporters on this site who have written and managed minor publications before, as well as a member or two have done it professionally. I wrote, edited, and helped managed production of the Buchtelite for nearly 3 years. Believe it or not, it took about $100,000 to operate per year (two semesters, twice-a-week); each issue would generate anywhere from $500-$1200 in revenue, a big chunk of the cost being printing/distribution. Needless to say, we had been losing money for years when I was there, well managed years before left us with a savings account with which to cover the gab. Advertising in publications just isn't what it used to be, and readership just isn't what it used to be.
I remember floating the idea (because I was desperate to come up with SOMETHING sports related that could generate revenue), and suggested summer issue or sports specific preview issue and stuff like that where we focus on selling to alumni/season ticket holders. We were met with resistance because of whatever company Athletics works with, because it would interfere with whatever they do (which is BS...we were a STUDENT publication). But secondarily no-one believed that there was enough buyers to cover the expense of publishing it in the first place.
To answer your last question, yes. Almost all of the major D-1 programs I've worked have a student newspaper/publication that produces their own magazine that they then sell to alumni subscribers, people on the street, etc, with season previews, team-by-team break downs etc. I know they exist, because I've worked with them before...Michigan, Ohio State, Penn State and Tennessee...providing them info on the Zips as well as photos (and credits) from my photographers. They sent us free copies in return...and they were marvelous, I was very jealous we didn't have something similar to it.
You have to ignore the "student" newspaper part...because people want to assume it's somehow not serious...they are. They're businesses, it's just the business is run exclusively by students of said university, as part of their bylaws. I'll pardon you guys the rant. Some are independent (like the Buchtelite Was).
Hope that was a little insightful?