UCB still has most undergraduates in liberal arts majors, including such majors as biology, economics, political science, etc… However, many of those choosing those majors have more pre-professional reasons for choosing them (e.g. pre-med, business/finance alternative, pre-law, etc.), similar to your examples of English and history majors looking to enter education.
But less selective schools like CSUs tend to have most undergraduates in overtly pre-professional majors like business.
This is also likely the case with private schools – the most selective ones tend to have many liberal arts majors, while the less selective ones tend to have more overtly pre-professional majors.