Any organization that relies on government money isn’t really a private organization. Colleges are probably the worst offenders: public money for private benefit.
I would point out, however, that the "private benefit" you cite is not what you think it is.
Financial aid and loan guarantees for college students have nothing to do with helping the students themselves. It's all about subsidizing the schools. That's why the government doesn't care if your major is electrical engineering, pre-medicine, or African Lesbian Studies.