The kinds of jobs that students can perform are not nearly the kind of jobs that a college with a physical plant to maintain, professors to pay, finances to administer, etc. can make a meaningful dent in. (By and large), students are not going to be doing electrical work, maintenance, financial accounting, administration, etc. -- the day to day necessary jobs that keep an institution running -- at all, or enough to be offsetting the costs of those professionals and paying for salaries of the faculty. And you wouldn't want students to be handling many of the jobs that rely on people to conscientiously do them for years, and have institutional memory in mind. They're there to be students, not workers. That's why most student jobs are of the type similar to dorm cleaners, kitchen staff, library, computer room, etc. -- short term temp work requiring no great specific skills.
The article itself acknowledges that much of the income comes from the endowment, grants, donations. If you wanted to start a school on the premise of student labor paying for it, without these existing sources, there would be no way. The cost of running a school is simply way too high in developed countries to do this.
Having students work is not a bad thing. But it isn't some utopian possibility to solve the problems of the cost of education at nearly any typical school. To make this possible you'd have to start something like an educational coop in a developing country. And I doubt that would be a significant contributor to higher education, until it got larger and more professional, at which point you would start to run into the exact same issues above.